Use a meat grinder, if possible, to grate the cheeses, using the cutter with large holes. Otherwise, use the coarse side of a cheese grater. Put the grated cheese in a mixing bowl and add half the juice from the canned pimientos. Dice the drained pimientos and add them along with the scallions.
Combine the mayonnaise, lemon juice, and garlic and add to the cheese mixture. Add the Worcestershire, Tabasco, and pepper and blend well.
Serve at room temperature as a spread for crisp crackers and raw vegetables or use as a sandwich spread.