Preheat oven to 350 degrees Fahrenheit.

In a medium pot, boil potatoes until soft, about 35 minutes.

While the potatoes cook: In a frying pan, melt two tablespoons butter. Add onions and sauté over a low flame until soft, about 15 minutes.

When the potatoes are done, drain. Add remaining two tablespoons butter and sautéed onions. Mash to combine.

Mix in one teaspoon salt, eggs, and potato starch. Add half the bag of cheese and mix well again.

Press mixture into a 9×13-inch dish or an oven-to-table dish. Bake 40 minutes, remove from the oven, and raise oven temperature to 400 degrees Fahrenheit.

Sprinkle remaining shredded cheese over the potatoes. Press the broccoli and cauliflower florets into the pan, standing up in neat rows or arranged to your liking. Sprinkle with salt and onion powder to taste, spray with cooking spray, and return to the oven.

Bake another 20 minutes or until vegetables look crisp.