Heat the oven to 400°F and cover a large baking sheet with parchment paper. The parchment keeps the delicate patties from sticking while their bottoms brown.
Steam or microwave the cauliflower rice for 2 to 3 minutes, just until tender, then cool it enough to handle and wring it dry in small batches with a cheesecloth or similar cloth. After squeezing, you should have about 154 grams or a little under 1 1/2 cups of cauliflower rice, with no water dripping from the cloth.
Put the dried cauliflower rice in a large bowl with the egg, mozzarella, parmesan, garlic powder, and black pepper, then stir until fully combined. The mixture should change from loose crumbs into a slightly sticky mass that clumps when pressed.
Pack the cauliflower mixture firmly into a 1/4 cup measuring cup, invert it onto the baking sheet, and gently flatten it to about 1/2 inch thick in an oval or rectangle. A compact shape should hold its outline instead of spreading across the parchment.
Shape the remaining mixture in the same way, leaving about 1 inch between each patty. Spacing gives the hot air room to brown the edges rather than trapping steam between the hash browns.
Bake for about 20 to 25 minutes, until the tops and edges turn golden, then leave the patties on the baking sheet briefly before lifting them. The browned perimeter should look firm, and the short rest helps the warm egg and cheese finish setting.