Slice rolls in half lengthwise and spread 1 tablespoon of mayonnaise on each half. Top each of the bottom halves with 1/2 cup pulled pork. Place 1/4 cup of pimento cheese dip onto each top half and close the sandwiches.
Heat a nonstick skillet or cast-iron pan over medium-high heat and add butter. When butter begins to bubble, add sandwiches to pan and cover with a heavy lid. Cook sandwiches over medium-low heat for 3 to 4 minutes per side.