1. Center a rack in oven and heat to 425 degrees. Without cutting all the way through, slice sub rolls in half lengthwise; set aside. Line a baking sheet with foil.
2. Place sausages on one half of prepared baking sheet and pierce all over with a fork; drizzle with 1 teaspoon oil and toss to coat. On empty half of baking sheet, combine pepper and onion slices, cherry peppers, pickling liquid, Italian seasoning, and remaining 2 teaspoons oil; season with salt and pepper. Toss veggies gently to coat, then spread into a single layer.
3. Transfer to oven and bake until sausages are cooked through, vegetables are tender, and everything is lightly browned, 15 to 20 minutes, flipping sausages and tossing pepper mixture halfway through. (If vegetables are browning too quickly, cover them loosely with foil for remainder of cook time.)
4. Remove baking sheet from oven and divide sausages and pepper mixture among rolls. Arrange subs on baking sheet and top each with a slice of cheese. Return to oven and bake until cheese is melted, 3 to 5 minutes. Sprinkle with basil and serve.
Source: Hannaford fresh Magazine, September 2020