Preheat oven to 400F.
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.
On a baking sheet, drizzle the eggplant with about 2-3 tablespoons EVOO and season with salt and pepper. Transfer to the oven and roast, turning occasionally until tender, about 20 minutes. Turn off the oven and turn on the broiler.
Add the roasted eggplant into the reserved tomato sauce and stir to combine. Sprinkle the sub rolls with some Parmigiano then place a heaping spoonful of the eggplant-tomato mixture onto the sub roll. Top with a slice or two of the 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.