Slowly add egg mixture to potato mixture in skillet and cook, stirring gently and smoothing around edges with a rubber spatula, until eggs are scrambled in spots, about 2 minutes. Transfer to oven and bake until center is just set, 16 to 18 minutes. Remove from oven and increase temperature to broil. Top frittata with remaining cheese. Return to oven and broil until cheese is bubbling and golden, 2 to 4 minutes. Let cool for 5 minutes before slicing. Frittata can be made up to one day ahead and stored once cooled, covered, in the refrigerator. Bring to room temperature and reheat, if desired.