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In the bowl of a food processor fitted with a knife blade, process cream cheese, mayonnaise, onion, garlic powder, salt, and pepper until smooth.
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Add the shredded cheeses and pimentos and pulse to combine. Do not over-process. Transfer pimento cheese to a bowl and stir if needed to combine ingredients thoroughly. Cover and chill for at least 3 hours.
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Heat a skillet or griddle to medium heat. Do not get too hot or it will burn the butter and bread.
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Butter one side of two bread slices. Spread a thick layer of pimento cheese on the un-buttered side of a bread slice.
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Place pimento cheese covered bread slice butter side down in the skillet. Cover skillet with a lid and cook for 1 minute.
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Remove lid and top sandwich with the other slice butter side up. Cook until bottom is lightly browned and toasted.
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Flip sandwich over and cook until the other side is lightly browned and toasted.
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Transfer sandwich to a plate and slice in half.
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Repeat with remaining bread and pimento cheese or grill 2 to 4 sandwiches at a time, depending on size of skillet. Do not over-crowd the skillet.
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Refrigerate extra pimento cheese for up to 5 days.