Preheat oven to 300 degrees F (150 degrees C).

Combine kosher salt, 1/4 cup black pepper, 1/4 cup Italian seasoning, rosemary, granulated garlic, granulated onion, 1 tablespoon red pepper flakes, and lemon pepper together in a bowl.

Place pork shoulder in a large roasting pan. Rub with lemon juice, 1 tablespoon olive oil, red wine vinegar, and Worcestershire sauce on all sides and between any crevices. Sprinkle with kosher salt mixture and rub over all sides. Pour white wine, chicken stock, and 4 crushed garlic cloves into the bottom of the roasting pan.

Cover pan tightly with heavy-duty aluminum foil and roast pork in the preheated oven until tender and a thermometer inserted reaches 200 degrees F (95 degrees C), 3 to 4 hours. Transfer pork to a cutting board and allow to cool slightly before pulling. Using two forks, shred the pork shoulder into bite-size pieces. Transfer meat to a large bowl and toss with some of the pan juices to keep it moist.

Increase oven temperature to 500 degrees F (260 degrees C).

Heat 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat; cook and stir goat horn peppers, red bell pepper, onion, 1 tablespoon Italian seasoning, 1 teaspoon red pepper flakes, salt, and black pepper in the hot oil until onion softens and begins to turn golden, about 12 minutes.

Stir in mushrooms, garlic basil spread, and Marsala wine and cook until wine has reduced and mushrooms have softened, about 5 minutes. Mix pulled pork and pesto sauce into vegetables and heat through, about 10 minutes. Spoon pork mixture into hoagie buns and top each with 1/2 cup mozzarella cheese.

Place sandwiches onto a baking sheet and bake in the hot oven until cheese is melted and bread is toasted, about 5 minutes. Top with cherry tomatoes and basil.