Preheat the oven to 450 degrees.
Line a baking sheet with parchment paper. Drizzle with a thin layer of oil and rub with your fingers or brush to grease the pan.
Combine the ground almonds, Parmesan and 1/2 teaspoon salt in a shallow bowl or plate with a fork. Beat the eggs in a second shallow bowl. Season the chicken generously with salt and pepper. Dip each breast in the eggs, and then the almond mixture. Press the crumbs into the chicken and make sure the breasts are well-covered, shaking off any excess. Place on the greased baking sheet.
Bake the chicken for 10 to 15 minutes, until the bottom crust has begun to brown (you'll see any crumbs on the pan have become golden). Carefully flip the cutlets with two flat spatulas, and continue to cook until the coating is golden brown and firm, 5 to 10 more minutes.
Meanwhile, heat 2 tablespoons of olive oil in a large saucepan. Cook the garlic and chili flakes, keeping an eye on it, until sizzling and beginning to turn golden brown, 1 minute. Add the tomatoes and 1 teaspoon salt. Simmer over medium heat, stirring occasionally, until soft and most of the liquid has been released, 10 to 15 minutes. Stir in half the basil and set aside.
Top the baked chicken with the mozzarella slices, tearing them into smaller pieces with your fingers, followed by the tomato sauce. Try to leave any loose juices in the pan so the cutlets don't get too soggy. Any remaining sauce can be served on the side. I like leaving a little crust around the edges naked - like a pizza!
Return to the oven and cook until the mozzarella is melted, 5 more minutes.
Garnish with the remaining basil and additional parm, if desired. Serve warm from the pan alongside any remaining sauce!