With a mandolin or a sharp knife, carefully cut the sweet potatoes into ¹⁄₁₆-inch (1 mm) thick slices.
Place the sweet potato slices in a large bowl, add the salt, pepper, paprika, garlic powder, and onion powder, and toss the potatoes until evenly coated.
Let sit for about 20 minutes, until water releases from the sweet potatoes and the slices are soft and flexible.
Brush the cups of a 12-cup muffin tin with the olive oil.
Arrange 5 sweet potato slices around the sides of a muffin cup, overlapping slightly. Place 1 slice on the bottom to create a flower. Repeat with the remaining potato slices. Sprinkle a bit of cheese in the bottom of each cup.
Bake for 10 minutes until the cheese has melted and the sweet potato slices are tender.
Remove the potato cups from the oven and reduce the oven temperature to 300°F (150°C).
Add your desired fillings to the cups. Season with salt and pepper.
Bake for another 20-25 minutes, or until the eggs are completely cooked and/or the vegetables are tender. Let cool for about 5 minutes.