Prepare the eggs: Slice the hard-boiled eggs in half lengthwise. Gently remove the yolks and place them in a bowl. Set the egg whites aside on a serving plate.
Make the filling: Mash the egg yolks with a fork until smooth. Add the mayonnaise, Dijon mustard, and a pinch of salt and pepper. Stir in the shredded Irish cheddar cheese and crumbled bacon (if using).
Fill the eggs: Spoon or pipe the yolk mixture back into the egg white halves. Make sure the filling is evenly distributed in each egg.
Garnish: Sprinkle the deviled eggs with smoked paprika and freshly chopped chives for a pop of color and flavor.
Serve: Serve immediately or refrigerate until ready to serve. These deviled eggs are best enjoyed chilled.