Add the cream cheese, mayonnaise, mustard, paprika, and garlic powder to the food processor. Puree until completely smooth, then add the shredded cheeses and diced pimentos. Pulse to combine, but do not puree.
Scoop (or pipe) the pimento cheese filling into the center of each egg white. Then top with fresh dill sprigs or chives as a garnish. Sprinkle with pepper if desired. Wrap well and refrigerate until ready to serve.