Preheat over to 375°F. Spray a 6-cup non-stick muffin tin with oil spray and set aside.
Toss grated sweet potato, thyme, 1/4 teaspoon salt, 1/8 teaspoon black pepper, onion powder and pecorino cheese (except for reserved 2 teaspoons) together in a mixing bowl to combine.
Divide potato mixture evenly into six portions (about 1/4 cup plus 1 tablespoon) and place each in a prepared muffin cups.
Press mixture into the bottom and up along the sides of each cup to form a well making certain there are no open gaps.
Spray the insides of the potato wells with olive oil spray. Transfer to oven and bake for 8 minutes.
Remove muffin tin from oven, gently press the bottoms of the sweet potato cups and crack an egg into each.
Return tin to the oven and bake until white are set and yolk are cooked, 12 minutes for runny eggs, 14 for slightly hardened yolks.
Let sit one minute before carefully removing using an off set spatula.
Sprinkle with remains remaining pecorino and more salt and pepper to taste if desired.