In a bowl, combine butter, water and vinegar. In a separate bowl, combine dry ingredients. Fold dry ingredients into wet mixture until a dough has formed. On a floured surface, roll out dough. Using a biscuit cutter or cup, cut 3-inch rounds from dough. Let dough rest in refrigerator for 10 minutes (so it can firm up a bit) before proceeding with recipe.
Make the empanadas:
In a large pot with high sides fitted with deep-fry thermometer, begin to warm peanut oil to 350 degrees.
While oil heats, assemble the empanadas: Remove dough from refrigerator and drop a couple tablespoons of pimento cheese into center of each round, taking care to leave a border. Fold dough over cheese to form a half moon, crimping edges with a fork to seal.
Fry empanadas in batches until golden brown, about 6 to 7 minutes.