Slice the hard-boiled eggs in half lengthwise. Scoop out the egg yolks and transfer them to a food processor or mixing bowl if you don’t have a processor; set the egg whites aside.
If using a mixing bowl, mash the egg yolks completely until they form a fine powder before adding the rest of the ingredients and mixing until smooth. If using a food processor, add all of the ingredients to the egg yolks (no need to process first), then process until smooth. If the mixture seems too thick, add a drizzle of olive oil. Taste and adjust seasonings as desired. If refrigerating at this point, keep in mind the flavors will mellow once refrigerated.
Use a piping bag with a large tip or a plastic bag with the corner snipped to fill the egg white cavity with the yolk mixture. Chill for 30 minutes, time permitting.
Sprinkle each deviled egg with crumbled bacon, chives and optional paprika or Cajun seasoning. Serve immediately.