Re: courgettes, not minor impediments...
Being vegetarian, a lot of my meals start off with a diced onion in a pan with a press of garlic, a splash of oil and a splash of water. It may end up as curry, risotto, stir-fry, spaghetti sauce, salsa, couscous, cottage pie, chilli or mousaka.
Courgette can go in any of that lot. The time to put the courgette in is at the start, with the onions.
But if you want to eat courgette as a vegetable, I'd recommend either slicing it lengthways to go in a stir-fry, frying it in butter or oil, or roasting it in the oven with some other Mediterranean vegetables.