Heat 1 teaspoon olive oil in a skillet over medium heat. Stir in mushrooms; cook and stir until mushrooms are tender, 5 to 7 minutes. Transfer the mushrooms to a bowl and set aside.
Heat the remaining 2 tablespoons olive oil in the skillet over medium heat. Add the pork chops, browning on both sides, 7 to 10 minutes. Place the pork chops on a plate, then drain all but 1 tablespoon of drippings from the skillet. Stir in the garlic and onion; cook and stir until the onion has softened and turned translucent, about 5 minutes.
Pour in the tomatoes, then season with basil, oregano, salt, and pepper. Transfer the pork chops back to the skillet; cover and simmer until the pork chops are tender and no longer pink in the center, about 45 minutes. Stir in some water if the mixture becomes too dry. Place the bell pepper on top of the pork, then add the reserved mushrooms. Continue to simmer until the bell pepper is tender, 5 to 10 minutes.