In a large pot or vegetable steamer, steam squash, cauliflower and garlic cloves until tender, 5 to 7 minutes. You may need to do this in batches, depending on the size of your pot.
Drain vegetables very well in a colander, shaking to remove any excess water, and then transfer half to a food processor. Puree until smooth and transfer to a large bowl, then repeat with remaining vegetables.
Stir half of the Parmesan, the cream salt, pepper and dried thyme.
Preheat oven to 350F. Transfer pureed vegetables to a 3 to 4 quart glass or ceramic baking dish and spread out smoothly. Top with remaining Parmesan and bake for 30 minutes.
Turn broiler on high and broil 5 minutes to brown topping.