Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.

In a large skillet, heat the olive oil over medium heat. Add the chopped onion and cook until softened, about 5 minutes. Add the ground beef and cook, breaking it up with a spoon, until browned. Drain off any excess grease.

Stir in the garlic powder, paprika, 1/4 teaspoon salt, and 1/4 teaspoon black pepper. Cook for another minute until fragrant. Remove from heat.

In a medium bowl, whisk together the beaten eggs, milk, remaining 1/4 teaspoon salt, remaining 1/4 teaspoon black pepper, and optional cheddar cheese.

Layer half of the thinly sliced potatoes in the prepared baking dish. Spread the seasoned ground beef mixture evenly over the potatoes. Top with the remaining potato slices.

Pour the egg and milk mixture evenly over the potatoes and meat. Ensure it covers the entire surface.

Bake for 45-55 minutes, or until the gratin is set, the potatoes are tender, and the top is golden brown and slightly puffed. Let it rest for 10 minutes before serving.