Preheat oven to broil (or 550°F).

Bring 1 inch of salted water to a boil in a large pot.

Add sliced carrots, green beans (cut into 1-inch pieces), cauliflower florets, and sliced onion to the boiling water.

Return to a boil, then reduce heat to a simmer.

Cover and simmer until vegetables are tender, about 12-15 minutes.

Drain the vegetables, reserving 1 cup of the cooking liquid.

Place the cooked vegetables in an ungreased 11x7-inch or 8-inch square baking dish.

In a saucepan, melt butter over low heat.

Whisk in flour, salt, and pepper until smooth.

Cook over low heat, stirring constantly, until the mixture is smooth and bubbly; remove from heat.

Stir in the reserved vegetable liquid and whipping cream.

Bring to a boil, stirring constantly.

Boil and stir for 1 minute; remove from heat.

Pour the sauce evenly over the vegetables in the baking dish.

Sprinkle grated Parmesan cheese over the top.

Broil in the preheated oven until the top is light brown and bubbly, about 3-5 minutes. Watch carefully to prevent burning.