Preheat broiler.
Place a medium-size skillet over medium heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the garlic to the pan and cook gently until aromatic and light golden brown, about 2 minutes. Add the sun-dried tomatoes, stock, some salt and pepper to the pan (the stock should cover the tomatoes) and simmer until the tomatoes have plumped up and softened, about 15-20 minutes. Add the can of tomatoes to the pan then transfer the mixture to a food processor and puree. Add chopped basil, season with salt and ground black pepper and reserve warm back in the skillet.
Return the sauce to the skillet and add in the rotisserie chicken. Simmer until the chicken has heated through, 2-3 minutes, then remove the pan from the heat and stir in the Parmigiano. Divide the mixture between the sub rolls and top with a slice or two of mozzarella. Pop the sandwiches under the broiler until the cheese is melted and golden brown.
Serve with a Romaine salad and a few olive oil potato chips alongside.