Slice the hard-boiled eggs in half. Pop the yolks with a small spoon into the bowl of a food processor, then add the Cheddar, sour cream, cream cheese, mayonnaise, mustard, relish, hot sauce and some salt and pepper. Run the food processor until smooth. Remove the filling to a bowl and fold in the pimientos.
Transfer the mixture to a piping bag fitted with a large star tip and pipe into the egg whites. Garnish with green onions, a dusting of paprika and crushed butter crackers.