Preheat the oven to 425°F (220°C). Pat the chicken breasts dry and season both sides generously with kosher salt and freshly ground black pepper.

In a large ovenproof skillet (12 to 14 inches wide), heat the olive oil over medium-high heat. Add the chopped onion and a pinch of salt, cooking for 2 to 3 minutes until the onion softens and turns translucent. Stir in the minced garlic, anchovies, oregano, fennel seed, and crushed red pepper flakes. Continue cooking for another 1 to 2 minutes, stirring constantly until the mixture becomes fragrant and the anchovies dissolve into the oil, creating a savory base.

Add the crushed tomatoes and roasted red peppers to the skillet, stirring to combine. Bring the sauce to a gentle simmer and let it cook for about 3 minutes to allow the flavors to meld together. Nestle the seasoned chicken breasts into the sauce, coating them lightly, then turn off the heat.

Transfer the skillet to the preheated oven and bake for 15 minutes. Carefully remove the pan, flip each chicken breast, and top evenly with shredded mozzarella cheese. Return the pan to the oven and bake for another 5 minutes, or until the cheese is fully melted and bubbly, and the chicken reaches an internal temperature of 165°F (74°C).

Remove the skillet from the oven and sprinkle the freshly chopped basil over the top. Let it rest for a couple of minutes before serving. Serve warm with a spoonful of the flavorful tomato-pepper sauce over each piece of chicken, paired with pasta, crusty bread, or a green salad for a complete meal.