Preheat the oven to 425 F. Spray a rimmed baking sheet with nonstick spray.

Slice the potatoes into 1-inch thick rounds.

In a large bowl, combine the melted butter, garlic, thyme, salt, and pepper. Toss the potato rounds in the butter mixture until coated, then place them on the baking sheet in a single layer with space between slices.

Bake for 25 to 30 minutes, until tender.

Remove the potatoes and change the oven setting to broiler. Use a potato masher, fork, or the bottom of a glass to gently smush the potatoes to about 1/2-inch thick.

Sprinkle the feta evenly over the potatoes. Broil for 2 to 4 minutes, until the cheese is melty and slightly browned.

Serve hot or warm, sprinkling red pepper flakes and parsley or scallions on top.