Preheat oven to 400°F. Grease muffin tins with cooking spray.
In a large bowl, combine minced garlic and shallots, cream, 1 cup Parmesan cheese, Gruyere cheese, salt, pepper, and thyme leaves. Set aside.
Using a mandolin or knife, slice peeled potatoes into 1/8-inch thick rounds.
Stack sliced potatoes into muffin tin cups, staying below the top of the tin.
Spoon the cream mixture into each cup. Potatoes should be completely submerged in the cream. Make sure cream does not overflow outside of the muffin cup.
Loosely cover pan with foil. Bake for 30 minutes.
Remove foil and sprinkle remaining 1/2 cup Parmesan cheese onto each stack of potatoes. Return to oven without foil and bake for an additional 10-15 minutes until potatoes are tender and cheese golden brown.
Allow to cool slightly. Using a butter knife, cut along the inside edges to loosen.
Gently lift stacks out, garnish with a small stem of thyme. Serve immediately.
Note. To make ahead, prepare recipe through steps 2-5....Tightly cover with plastic wrap and store in the refrigerator up to 1 day.