As for me, I´ll just reflect on shapes and sizes. Isn´t it odd that things taste different if they´re cut different? I hate carrots cut in coins. They remind me of the flabby, overcooked, tasteless stuff I refused as a child. If I´m having them sauteed or roasted or plain steamed, or they are to go into a stew, it has to be thick batons. I grate them for salads, or make long slivers with the peeler, and these are the shapes I like in a stirfry. For soups I favour the small cube, or the very small cube for my baby. And if I´m in a tearing hurry, I grate it with a microplane so it cooks in her soup truly fast. Long sticks are my favourite snack (never mind that they´re healthy, I just love them).
Here´s a quick side dish preparation for carrots:
Take a couple of carrots cut in thick batons, and put them in a small non stick frying pan with water to come half way up (this is very little water) and a small piece of butter, the size of a hazelnut, no more. Salt, fire it up and get on with the rest of dinner. When it comes to boil, cover it and let them steam. In a few minutes they´ll be quite soft, and the liquid should have evaporated, but if it hasn´t, take the cover off and let it bubble up.
Sometimes I add french green beans too, straight from the freezer, and they cook at the same time.