Sauté onions in butter til translucent. Add garlic.

Slowly add half and half and chicken stock.

Mix cornstarch with a little water until no clumps. Then add to pot.

Add nutmeg and bay leaves. Cook on medium low until thickened.

Add carrots and broccoli. Simmer until tender.

Discard bay leaves. Add cheese. Stir until melted. Season with salt and pepper.