Preheat oven to 400 degrees F. Transfer asparagus to an oval 9"x13" baking dish. Sprinkle with the slivered garlic, salt, pepper, red pepper flakes, and fresh thyme. Gently toss the asparagus to distribute the garlic evenly among the layered asparagus spears.
Drizzle the heavy cream over the asparagus and sprinkle with the mozzarella and Parmesan cheese. Gently shuffle the asparagus spears to distribute some of the cheese among the lower layers of the asparagus.
Transfer to the oven and bake for approximately 20 minutes, or until asparagus spears are tender and cheese is melted.
Set oven to broil. Allow the cheese to broil for 1-2 minutes or until golden and bubbly. Remove from the oven and allow to cool for 1 minute. Best enjoyed immediately.
Feel free to substitute the heavy whipping cream with half and half, if desired.