You can grate them and add then raw, or you can precook them. For cooking all vegetables, use any technique you like - saute, steam, boil, bake, or grill them. Next mash, puree, chop or dice them. Either use each vegetable on its own or combine it with others as a medley. To give the kugel body, add a small amount of bread crumbs, cracker crumbs, cooked rice, or potato.
Some people turn to the box of matza meal that's usually in the pantry.
After all, it's not just for making matza balls. Of course, you can combine the two basic types, a noodle kugel and a vegetable kugel. By mixing or layering the vegetable with the noodle mixture, you make the kugel more satisfying. It's more kid-friendly, too. If you're trying to get your family to eat broccoli, you can hide it in a kugel.