Almost everyone intends to eat more vegetables and almost nobody manages it by buying more of them. The vegetables arrive, sit in the drawer, and leave in the bin. The problem is not intention or availability. It is that vegetables are treated as an additional dish rather than as part of what is already being cooked.
Add, do not add on
A separate bowl of steamed greens beside the meal is the version everybody skips. Vegetables that are inside the dish get eaten without any decision at all. Grate a carrot into a bolognese. Throw spinach into the pan in the last thirty seconds. Put half a cabbage through a stew. Add frozen peas to rice, pasta, curry, soup and anything else that is already wet. None of that is a vegetable side dish; all of it is more vegetables.
Cook them so they taste of something
Boiled vegetables are the reason people believe they dislike vegetables. Roasting, frying and charring make the same vegetable sweet and savoury instead of watery. High heat, oil, salt and space in the pan. That is the whole technique, and it turns broccoli, cauliflower, carrots, sprouts and cabbage into things people go back for seconds of.
Put a sharp thing on top
Vegetables are mild, so they need contrast: lemon, vinegar, yoghurt, chilli, a pickle, a hard cheese, toasted nuts or seeds. A roasted vegetable with nothing on it is fine; the same vegetable with acid and crunch is a dish. This is the single most effective change most people can make, and it takes ten seconds at the end of cooking.
Make them the first thing on the plate
If the vegetables go into the pan first and everything else joins them, the proportions take care of themselves. If they are the last thought, there is no room left. It also helps to buy fewer kinds and more of each. Three vegetables you will genuinely use beat seven that look virtuous in a basket and rot in a drawer.
Frozen and tinned count
Frozen peas, spinach, beans and sweetcorn, and tinned tomatoes, chickpeas and lentils, are all vegetables. They do not become less nutritious for being convenient, and they are the reason an empty fridge still contains a decent meal. The best vegetable is the one you will actually eat this week. Everything else is a good intention slowly turning to liquid at the bottom of the fridge.
Put them in the dish rather than beside it, roast or fry rather than boil, finish with something sharp, and count the frozen ones. That is how the amount goes up without anybody deciding to eat more vegetables.