Prep and Sear the Pork: Sprinkle the pork chops with salt and pepper and dredge in the flour. Heat 2 tablespoons of olive oil in a large skillet. When the oil is shimmering, add the pork chops and cook for 2 to 3 minutes on each side or until browned. Transfer the chops to a plate and set aside.
Sauté the Vegetables: Heat another tablespoon of olive oil in the same skillet over medium heat. Add the onion and mushrooms to the pan and cook for 4 to 5 minutes or until the onions are translucent. Add the bell pepper and garlic and cook for 2 minutes longer.
Make the Sauce: Add the tomatoes, chicken broth, and wine to vegetables in the skillet, scraping the bottom of the pan to get the browned bits. Stir and bring to a boil. Add the tomato paste and simmer for 2 minutes.
Finish the Dish: Add the pork chops back to the skillet, cover the pan, and simmer for 15 to 20 minutes or until the sauce is slightly thickened and the chops are cooked to at least 145 F.
Serve: Transfer the chops and sauce to a serving platter and top with parsley. Serve along with rice, pasta, or potatoes.