In a large skillet, brown chops over medium-high heat. Transfer to slow cooker.
In the same pan, cook onion in oil over medium heat until browned. Stir in mushrooms and bell pepper, and cook until these vegetables are soft. Mix in pasta sauce, diced tomatoes, and white wine. Season with Italian seasoning, basil, and garlic. Pour over pork chops in slow cooker.
Cook on Low for 7 to 8 hours. To serve, place a slice of cheese over each chop, and cover with sauce.