In a bowl, mix together the olive oil, tomato paste, minced garlic, Italian seasoning, dried oregano, dried basil, salt, and black pepper until smooth and well combined.
Add the butterflied chicken breasts and coat them well in the marinade. Make sure every piece is fully covered. Cover and marinate for at least 30 minutes (or up to overnight in the fridge for deeper flavor).
Place a large skillet or frying pan over medium-high heat. Add 1–2 tsp olive oil and let it heat until hot and shimmering. Add the chicken to the hot pan in a single layer. Cook uncovered for 5–7 minutes on the first side until golden and nicely seared. Flip the chicken and cook for another 5–7 minutes on the second side over medium heat.
Lower the heat to medium-low, cover the pan with a lid, and cook for another 2–4 minutes. Covering the pan for the last few minutes helps keep the chicken juicy while it finishes cooking.
Remove the chicken from the pan and let it rest for 5 minutes before slicing. Serve warm with rice, roasted vegetables, or a fresh salad.