Baking bread ... without crust?

No, I don't think it's possible to do that. At least, baking in a traditional way. Your oven should be higher than 300F to bake and the bread will be done when you reach 205F or so. The crust is formed because it takes more heat, sugars caramelize, etc.

There are a few things to have in mind to get a better crust, in the traditional sense, like moisture in the oven. If you want to avoid that kind of crust, don't add moisture and stop baking as soon as the bread is done.

I think your best bet is to find uses for the crust. There is a variation of gazpacho called salmorejo (at least in some parts of Spain) which uses only tomatoes, olive oil, garlic and leftover bread which is where my bread leftovers end.

I'm no expert on this, but from what I understand crust thickness is predominantly effected by the early stages of cooking. If there is a lot of steam in the oven initially it gelatinises the exterior and then this dries out giving a thicker crust area. The initial heat makes a large difference, if there is great heat initially, if you use a baking stone for instance, or pre-heated tins, the crust will be thicker as the heat penetrates further. Once the crust has formed you see, it is effectively self-limiting, shielding the rest of the loaf from the intensity of the heat. Do you coat your loaves before cooking? Some coatings enhance the crustiness, like salt-glaze.

Some tests may be in order, varying steam and initial heat to see what works best.

Like all cooking, what you put in and how you cook it will change the finished product. Different flours make different crust strength. Try more whole wheat ground flours, more roughly ground flours (stone mill etc). This keeps more starch bound up in the flour, and not floating about to make a hard surface. Using a mix of non-wheat flours will also change the crust, e.g. a 50/50 mix of whole wheat and corn meal will give a very soft crust

Try boiling or steaming your bread first, it may take a few hours of streaming to reduce the baking time by half, and hence a softer crust

Cover the top of the bread with with a piece of aluminum foil, just a rectangle the shape of the pan, not a cover

You can't bake bread to end up without crust, as it will always require high temperatures that will toast the outside (to varying degrees) without just dessicating the entire lump of dough.

For pure crustless bread, I would try to make something like a giant steamed dumpling. There are a few examples (courtesy Jefromi and Jay's comments, respectively) of this in Chinese cooking: baozi, a filled dumpling using yeast dough; or the larger mantou, similar but without filling.

When steaming dough it will retain much more (nearly all) water, so a drier dough would be in order. Generally in most bread-baking, the goal as Julio mentions is to get the inside to 200-210 °F, and by using steam at ~212 °F, you will get virtually no browning.

That said, crust can vary wildly, from very soft to very hard. The softer crust breads I bake are usually done in pans at lower temperatures (325-375 °F) and often contain milk, eggs and or fat. The more "crusty" breads are usually baked quickly at hot temperatures (>450 °F), but if done lower and slower it will change the crust significantly.

I don't know about truly crustless, but there's a style of loaf that's baked in a sealed 'pullman' loaf pan that's supposed to give a "nearly crustless" loaf:

http://www.cooking.com/products/shprodde.asp?SKU=159081&CCAID=FROOGLE159081

You can also make bread in a tin can so there's less crust formation:

http://thethingsilovemost.blogspot.com/2010/05/crustless-bread-whod-have-thought.html

Microwave bread recipes such as this Microwave English Muffin Bread should produce relatively crustless loaves, shudder.

Peeling the bread after you bake it sounds like the best bet. Still wastes the crust, but you can eat the crust and then tell your fiancee you finally baked her crustless bread.

If your fiance cuts crust off the softest of (commercial) breads, there's no way to make a totally crustless bread. You can store your home baked breads in a plastic shopping bag, which will make the crust very soft. You could also save all the off-cuts of crust in an open container to dry them out, to make breadcrumbs later. Then use the breadcrumbs as an ingredient of a meal and let her (later) know that she just ate all her crusts.

Yes, crustless bread is possible. And - it's easy! You'll use two cylindrical pans like this one ( https://www.amazon.com/Nordic-Ware-Cinnamon-Bread-Almond/dp/B00FLZLBS4) It will take a couple tries to figure out the best amount of bread that will fill the pan without overflowing, but underfilled or overfilled pans are aesthetic issues, not taste issues. And you'll use 2-3 pieces of wire, wrapped around the sides of the 2 pans to hold them together, making a cylinder to hold the bread. Then, bake as usual. Boom. Crustless bread. Happy fiance. You're welcome.

It's not a method suitable for home baking, but the bread used to make Panko breadcrumbs is cooked by passing an electric current through it and forms without a crust. You can see the apparatus used and the finished product in this YouTube video: https://youtu.be/uFbQuHE4z7g