Add eggs to a saucepan and fill the pot with water to ½-inch above the eggs. Over high heat, bring the water to a rolling boil, then cover, remove from heat. Let the eggs stand covered for 15 to 17 minutes.
Fill a medium bowl with ice water and transfer the eggs to the ice water for 5 to 10 minutes. Peel the eggs under running cool water.
Add the eggs to a food processor and pulse a few times until chopped. Add cream cheese, mayonnaise, sour cream, relish, vinegar, mustard, onion powder, and salt. Pulse until smooth, scraping the bowl as needed.
Spoon into a serving bowl and garnish with a sprinkle of paprika.
