Place 1 dozen eggs in a large pot. Fill the pot with cold water until it covers the eggs by about an inch. Bring the water to a boil; then reduce to a low simmer for 15 minutes. Remove the pot from the stove and place it in the sink. Run cold water into the pot for several minutes until the pot is full of cold water. Remove the eggs. Roll each egg to crack the shell and gently peel.
With a sharp knife, cut each egg in half length-wise. Remove the yolks and place them in the food processor. Add the mayo, mustard, dill, shallots, paprika, salt, and pepper to the egg yolks. Puree until extremely smooth.
Using a pastry bag and tip, or a zip-bag with one corner snipped off, pipe the yolk mixture into the hole of each egg. Sprinkle a few capers and extra chopped dill on each egg. Cover and refrigerate until ready to eat.