Stir the cheddar, pimentos, mayonnaise and garlic powder together until thick and evenly combined.
Season the flat iron steak with salt and black pepper.
Heat the oil in a cast-iron skillet over medium-high heat and sear the steak for 4 to 5 minutes per side until it reaches 145°F.
Rest the steak for at least 3 minutes, then slice it thinly across the grain.
Toast the split potato rolls cut-side down in the skillet for 1 to 2 minutes, then divide the steak among the bottoms.
Spread 3 tablespoons pimento cheese over each pile of steak and broil for 1 minute until softened and lightly bubbling.