Preheat the oven to 400°F. Lightly grease a 12-cup muffin tin with cooking spray or a little butter.
In a large bowl, whisk together the melted butter, garlic powder, onion powder, paprika, salt, and pepper.
Stir in the shredded cheddar cheese until evenly combined.
Add the potato slices and toss gently until all slices are evenly coated in the butter-cheese mixture.
Stack the coated potato slices into each muffin cup, filling them just above the rim. (They will shrink as they cook.)
Cover the muffin tin with aluminum foil and place on a baking sheet. Bake for 30 minutes.
Remove the foil and continue baking, uncovered, for another 30-35 minutes, or until the tops are golden and crispy and the potatoes are tender.
Let the stacks cool for 5 minutes, then run a butter knife around the edges to loosen each stack.
Serve warm, with a light sprinkle of kosher salt and chopped parsley, if desired.