Preheat the oven to 375 degrees F (190 degrees C).

Heat a large skillet over medium-high heat. Cook and stir beef in hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Add spaghetti sauce and garlic powder.

Mix rice, eggs, and 1/4 cup Parmesan cheese in a bowl. Mix 2 cups mozzarella cheese, cottage cheese, and 1/4 cup Parmesan cheese in another bowl.

Spread 1/2 of the rice mixture in a 3-quart baking dish, followed by 1/2 of the cheese mixture and 1/2 of the meat sauce. Repeat layers. Sprinkle remaining 1/4 cup Parmesan cheese and 1/4 cup mozzarella cheese over final layer of meat sauce.

Bake in the preheated oven until cheese is melted and sauce is bubbly, 20 to 25 minutes.