Carrots are rich in beta-carotene, a vitamin responsible for their orange colour. Moreover, once ingested, this molecule turns into the precious vitamin A. In carrots, beta-carotene is stored inside the cell wall, a bit like if it were sealed in small bags. The cell wall of plants, however, does not always break down during digestion, so part of the beta carotene is excreted... as you know.
The heat from cooking, on the other hand, is able to break down the cell wall and thus release all beta-carotene. This means that the same portion of carrots, if cooked, provides us with more vitamin A. We’re not talking about a specific or complicated cooking method: cut the carrots into slices and sauté them in a pan with a knob of butter or olive oil, and flavour with a clove of garlic and a pinch of salt and pepper. If you don't like them too crispy, you can put them in the microwave before cooking in the pan.
It will be less difficult for you to accept the fact that zucchini or courgettes also benefit from cooking, for the same reasons. After all, it is much less common to eat them raw.
There’s a third type of vegetable (we know, technically it's a fruit) that it’s recommended to eat cooked: tomatoes. In this case, the molecule released with heat is called lycopene, which always falls into the category of carotenoids. Furthermore, don’t forget two other even healthier cooked vegetables: spinach and asparagus.
At this point another question arises: should we cook all vegetables, then? Of course not. Those rich in vitamin C, for example, are recommended to be eaten raw, because this molecule tends to be destroyed by heat. And here there is room for another revelation: Brussels sprouts, which some people love cooked with a lot of excellent butter, fall into the same category. Nobody forbids continuing to eat them like this (they are so good!), but if you’re interested in the vitamins, it is better to cut them into very thin slices and put them in salads.
There is really no peace for health-conscious people, and this is even more true when we think of peppers. These vegetables are so rich in excellent nutrients that they have large quantities of both vitamin C and carotenoids. So, what should we do with these? The ideal method would be quick steaming, in order to both free the precursors of vitamin A, and respect vitamin C.