Warm oil in a large broilerproof skillet over medium heat. Add leeks, salt and pepper; toss to coat. Cover and cook, stirring often, until softened, about 10 minutes. Uncover and cook, stirring occasionally, until tender and glossy, 10 minutes longer. Transfer to a plate; let cool slightly. Rinse and dry skillet.
Preheat broiler. In a bowl, combine mayonnaise, mustard and chipotle. Stir in Cheddar, pimentos and leeks.
Spread 1 tsp. butter on 1 side of each bread slice. Sprinkle with Parmigiano-Reggiano; press to adhere. Flip bread; spread with pimento cheese. Place sandwiches in skillet, pimento cheese--side up. Cook over medium heat until bottom is golden, 2 to 3 minutes. Transfer skillet to oven. Broil until bubbling and browning in spots, about 2 minutes. Serve.