Preheat oven to 400°F. Combine the cheese, salami, onion, parsley, garlic and chile in a small bowl. Pound the chicken slightly and lightly season with salt and pepper. Arrange the cheese-salami mixture over half of each chicken breast. Fold the other half over and secure with toothpicks if necessary.
In a large skillet, heat the EVOO, 2 turns of the pan, over medium-high heat. Add the chicken and cook, turning once, until browned, about 5 minutes. Transfer the chicken to a baking sheet; place in the oven and cook through, 10-12 minutes. Let rest briefly, then slice crosswise.
Meanwhile, pour the wine into the skillet to deglaze the pan. Stir in the tomatoes and chicken stock. Cover the skillet and simmer over medium-low heat for 10 minutes. Top the chicken with the sauce and basil; serve with the crusty bread for mopping.