Remove the vegetables from the water and puree them, garlic included
Pour that puree into a pot and cook on low until the juice dries out
Incorporate the cornstarch and mix well
Season with salt and pepper
Add the cream and the grated cheese
Season to taste
Mix until the cheese has fully melted
Remove from stove and transfer to a buttered baking dish
Top with some more grated cheese
Baked for about 30 to 45 minutes until the puree stops bubbling
Notes
Carrots tend to give out a lot of water. It is thus important to try not to blend it with too much water, and to cooked down the pureed vegetables so as to allow some of the juice to absorb before seasoning and baking.