Cream separates to oil when heated

Generally if the cream separates, that means you've heated it too much -- either too hot, or too long.

Also, if you're making a cream-based pasta sauce, the standard method is to add the cream last to the other cooked ingredients in the sauce. That way you're less likely to overcook the cream. Most cream-based pasta sauces start with a base that has solids and oil, such as a white roux or a pesto, which further helps the cream hold together.

It seems that you got pure cream which has stood around for a few days. Cream is not a terribly stable emulsion, and the butterfat tends to rise to the top. When you heat it, it separates.

Try to buy a different brand which uses stabilizers, or add your own stabilizers (some starch might work if you don't have anything fancier), or use fresher cream. All will give you a smooth sauce.

That layer of oil is known as purified butter. In India it's known as ghee. We use that in cooking, it's better and healthier than processed oil that you get in the market.

If you put uncooked heavy cream in your coffee, you see the same thing (oil in the cream floats to the top). I am not convinced that the oil that you are seeing has anything to do with cooking.