Butter 1 side of each bun. Lay 3 slices butter-side down on a work surface. Top each with 4 slices of cheddar. Top with the other half of the bun, butter-side up.

Heat a cast-iron griddle over medium heat. Add the sandwiches and cook until the cheese begins to melt and the bread is golden brown, 2 to 4 minutes. Flip and continue to cook until golden brown and the cheese is melted through, 2 to 4 minutes. Cut in half and serve.