Slice beer bread into 1/2-inch slices and brush one side of each slice with melted butter.
Heat the cast-iron grill pan over medium high heat until it begins to smoke.
Grill each slice for about a minute and a half or until well-marked by the grill pan, then give each slice 1/4 turn and grill another minute if you want those cross-hatched grill marks. Repeat until all slices are grilled.
Spread two spoonfuls of pimento cheese on a slice of the grilled bread, top with tomato, salt and pepper to taste, a little arugula, and then crown it with another slice of grilled beer bread.