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 to grease the pan.
Combine the ground almonds and Parmesan in a shallow bowl. Place the beaten eggs in a second 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 1 minutes, until the coating is beginning to brown. Carefully flip, and continue to cook until the chicken is firm and cooked through, 5 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, about 15 minutes. Smush the tomatoes with the back of your spoon or spatula while cooking to release the juices. Stir in half the basil and set aside.
Top the baked chicken with the mozzarella slices, followed by the tomato sauce. Alternatively, you can transfer the chicken to the skillet, nestle it in the sauce and top with the cheese.
Return to the oven and cook until the mozzarella is melted, 5 more minutes.
Garnish with the remaining basil and serve immediately.