With the rack in the middle, preheat the oven to 425 degrees Fahrenheit. With a fork, combine the cheese, mayonnaise, and garlic in a mixing bowl. Add the mozzarella, Parmesan, and spinach leaves, diced.
Cut the chicken into three-quarters-slits without completely slicing it, and then spread it out on a level surface. Place a fourth of the mixture into each chicken breast before sealing it with a toothpick. Make sure the chicken breasts are flat on both sides so they can be seared.
With 3/4 teaspoon salt, 1/2 teaspoon pepper, 1/2 teaspoon garlic powder, and 1/2 teaspoon paprika, or to taste, season the exterior of the whole chicken breast.
In a large, heavy-bottomed pan or an ovenproof skillet made of cast iron, heat 1 1/2 teaspoons of olive oil over medium heat. Cook the chicken for 4 minutes on each side, or until golden brown, after adding it to the pan.
After a second flip, place the pan right away in a preheated oven. A thermometer put into the thickest part of the chicken stems should read 165°F after 10 to 15 minutes of baking at 425°F. Before slicing the chicken, let it for five minutes to sit. To serve, drizzle juices over the chicken.