How do I make my blended soup a more appealing colour?

Of course “appealing” is quite opinion-based, so let’s look at the problem in a slightly more neutral “how can I avoid the colors mixing when I blend the soup”.

In short, you can’t.
If you have a significant amount of green and red veggies, that is.

One of the appeals and key features of a classic minestrone are the colorful ingredients that give you a bright and versatile palette, almost a mosaic in a bowl. But let’s not argue with the question’s premise.

If you want to blend the whole soup, you need to stay in a limited range of the color wheel, which means for your soup everything that’s between red (as dictated by the tomato base) and yellow will be fine, as is white or translucent. Stay away from green. Blueish ingredients are quite rare and not part of a minestrone, so we can ignore that. In your example recipe, the spinach is out.

Alternatively you can blend everything except “the green”. That means you need to either fish out all the green vegetables or cook them separately. That said, the spinach in your recipe will cook so quickly that you could even add it after the blending step. And of course you still get chunks in the purée.

If your desire to blend is not motivated by the desire for a chunk-free result but about thickening the soup, you could use alternative ways to thicken the soup. An easy way would be to scoop out a few of the starchy ingredients (e.g. the potatoes), mash them up and put them back. Or introduce an additional thickener, e.g. a starch slurry.

The Turquoise Room (at the La Posada Hotel in Winslow, Arizona) has a "signature soup", which is actually two soups ladled into a single bowl: a bright yellow corn soup, and a darker brown bean soup.

While I kind of feel like this defeats the purpose of a minestrone (which, as far as I am concerned, is meant to show off the lovely vegetables), I wonder if a similar strategy might work here? Split the recipe into two soups: one which contains the red ingredients, and one with the green ingredients. Blend the soups separately, and them ladle them side-by-side into a shallow bowl to serve.

My guess is that you will need to reduce the amount of liquid in the soup to make this work—the goal is to end up with products at the end which are thick enough to remain separate after being served. The starch in the potatoes should also help (e.g. make sure that you are using potatoes in your recipe).

I sometimes use a sweet, mild paprika to redden tomato-based soups which have turned out too brown. It doesn't go with every flavour, of course, but it works very well to liven up the appearance.

A couple suggestions:

Blend only part of the soup: When you're done cooking it, remove half of the soup from the pot and blend it, then combine the blended portion with the unblended. The texture will be smoother than it would have been, but you'll still have recognizable whole pieces of veg and greens (which you should have in a minestrone).

Cover it up with toppings. Fresh green herbs like parsley add color without changing the flavor too much. Green pesto. Croutons, while they're still probably a shade of brown, will at least break up the visual of an expanse of brown soup. Thinly sliced cherry tomatoes, pomegranate arils, toasted tortilla strips, avocado chunks, diced red onion or cabbage, brightly-colored pickles, oil infused with turmeric or paprika, all make great soup toppings depending on the soup you're making.

You didnt said what is used in those soups.

Anyway, does the tomato base need to be cooked so long ? maybe you could cook the hard to cook veggies(like beet ,potatoes, carrots) on water first and only add the tomato in the end, that way the tomato will be fresher, more red, and more healthy too.

If you are using broccoli, leafes, greens vegetables and thats turning brown too you could try to add sodium bicarbonate in the water that cooks it. it helps to keep the green color. people use it for that and works well. I, particularly, dont like to add unnecessary chemicals to my foods. I prefer to time the cooking of the the veggies just in time to cook and avoid leaving too much longer for not overly cook the foods that would make colors fade, vitamins to decrease and cause the veggies to became too humid(in that thing, for being a soup, if you wait too long to eat it will be very humid/soft/"watery" anyway).

And just to resume and clarify, i see most answers are agreeing in your teory of the green veggies be the ones turning your soup brown but it is not the case. when you use green veggies in a white soup it doesnt turn green, because most of then do not color the food like that, like a beet or the tomato itself. what turn tomato bases brown is overcooking or the tomatoes being too old