Fill a large pot halfway with water and bring to a boil over high heat.
Once water is boiling, carefully place eggs into the pot, and cook eggs for 10 minutes. Once cooked, drain and rinse eggs under cold water.
Remove the egg shells and split each egg in half length-wise.
Remove the yolks from each egg half and place them (yolks) in the bowl of a food processor (or a bowl big enough to mix in).
Add Arbequina EVOO, Dijon mustard, salt, capers, and lemon juice to the bowl and blend/mix until smooth. Transfer the mixture to a piping bag (or you can just scoop with a spoon).
Place eggs on a platter or plate and fill each half evenly with the yolk mixture. Top devilled eggs with pepper, paprika, and fresh dill before serving.