Preheat oven to 350°F (175°C). Cut pork loin into 3-4 large pieces. If using bone-in pork, remove and discard bone. Season pork generously with salt and pepper.
In a large bowl, combine thyme, oregano, rosemary, garlic, and chopped onion. Rub the spice mixture all over the pork pieces, ensuring even coating.
Place pork in a large ovenproof skillet or Dutch oven. Pour in the broth and crushed tomatoes, ensuring the pork is mostly submerged. Cover the skillet tightly with a lid or aluminum foil.
Bake for 3-4 hours, or until the pork is fork-tender and shreds easily. Check on the pork halfway through cooking and add more broth if needed.
While the pork bakes, prepare the peppers and onions. Heat olive oil spray in a large skillet over medium heat. Add the sliced peppers and onions, and cook until softened and slightly caramelized, about 5-7 minutes. Season with salt and pepper to taste.
Once the pork is cooked, transfer it to a cutting board and shred it with two forks. Discard any large pieces of fat.
Add the shredded pork to the skillet with the peppers and onions. Heat through for about 5 minutes, allowing the flavors to meld.
Sprinkle the shredded mozzarella cheese over the top of the skillet. Cover and cook for 2-3 minutes, or until the cheese is melted and bubbly.
Serve the Italian pulled pork skillet immediately, garnished with fresh basil and a drizzle of your favorite sauce, like BBQ sauce or salsa.