Place the eggs in a large pot and cover with cold water. Place over high heat and bring to a boil. Let the water boil for one minute, then remove from the heat and cover the pot. Let sit for 10 minutes, then drain and run cold water over the eggs until they are cool to the touch.

Peel the eggs and cut into half horizontally. Remove the yolks.

Place the ham, mayonnaise, relish, Dijon, Worcestershire sauce and hot sauce in a food processor. Season with salt and pepper. Pulse a few times to combine and start breaking down the ham. Add half of the egg yolks. (Reserve the remaining yolks for another use.) Continue to pulse until you reach your desired consistency.

Transfer the ham mixture to a large ziptop bag. Cut off the corner and squeeze some of the ham mixture into each of the egg whites. Top with fresh snipped chives.