Using a sharp knife, cut each chicken breast horizontally through the middle, keeping the two halves connected.
Season the inside and outside of each fillet with salt and pepper. Cut the Gorgonzola into 4 slices.
Brush one half of each fillet with tomato paste. Top with a slice of Gorgonzola and 3 basil leaves. Fold the fillet closed and wrap 2 bacon slices around it, securing with toothpicks if needed.
Cut the red pepper, green bell pepper, and onion into small cubes. Mince the garlic clove.
Heat olive oil in a large pan over medium-high heat. Fry the wrapped fillets until golden, then reduce heat to medium and cook for another 5 minutes. Transfer to a plate and keep warm.
Add a small amount of olive oil to the same pan. Sauté the onion and garlic over medium heat for about 2 minutes until softened. Add the pepper cubes, 1 tablespoon thyme, and 1 tablespoon oregano (dried or fresh). Pour in the vegetable broth and bring to a boil. Stir in the canned tomatoes and season with salt and pepper to taste.
Place the fillets on top of the vegetable mixture. Cover and simmer for 25 minutes until the chicken is cooked through (74 °C / 165 °F internal temperature). Remove fillets and adjust seasoning of the sauce to taste.