Add 1 tray of ice cubes to a large bowl and fill with water. Fill a large pot with 1 inch of water. Place steamer insert inside, cover, and bring to a boil over high heat. Add eggs to steamer basket, cover, and continue cooking over high heat for 12 minutes. Immediately place eggs in bowl of ice water and allow to cool for at least 15 minutes before peeling under cool running water. Slice each egg in half lengthwise.
Place all yolks in the bowl of a food processor. Select 16 of the best-looking egg white halves and set aside; reserve remaining 8 for another use. Add mayonnaise, Herkner Farms Champagne Dill Honey Mustard, 1/2 tablespoon vinegar, and hot sauce to food processor and process until smooth, scraping down sides of bowl as necessary.
With machine running, slowly drizzle in 2 tablespoons olive oil. Season mixture to taste with salt and remaining vinegar. Transfer to a zipper-lock bag. Filling and egg white halves can be stored in the refrigerator up to overnight before eggs are filled and served.
Cut off a corner of zipper-lock bag and pipe filling mixture into egg whites, overstuffing each. Drizzle with remaining olive oil and sprinkle with black pepper, chives, crushed red pepper or paprika, and sea salt. Serve immediately.