Preheat your oven to 375°F (190°C). This ensures that your stacks will cook evenly and develop a beautiful golden color.
Generously grease your muffin tin with olive oil using a pastry brush or cooking spray. This will help the stacks release easily once baked.
Thinly slice the Yukon Gold potatoes to about 1/16 inch thickness. You can use a sharp knife or a mandoline slicer for this. Uniformity is key for even cooking.
In a mixing bowl, combine the olive oil, paprika, cayenne pepper, minced garlic, fresh thyme leaves, lemon juice, salt, and black pepper. Mix well to create a flavorful oil.
Begin layering the potato slices in the greased muffin tin. Start by stacking a few slices in each cup, drizzling some of the seasoned oil mixture over each layer. Sprinkle a bit of shredded Parmesan cheese between the layers for added flavor. Continue layering until you fill each muffin cup, leaving a little space at the top.
Place the muffin tin in the preheated oven and bake for about 30-35 minutes, or until the tops are golden brown and the potatoes are tender. A toothpick should easily pierce through the center of the stacks.
Once baked, remove the muffin tin from the oven and let it cool for a few minutes. Use a spoon or a small spatula to gently lift each potato stack out of the tin. Garnish with additional thyme and Parmesan cheese before serving.