Place eggs in a pot and cover with cold water by about an inch. Bring to a boil over high heat, then remove from heat, cover, and let sit for 7 minutes. Transfer eggs to a bowl of ice water to stop the cooking process and cool completely, about 5 minutes. This ensures perfectly cooked hard-boiled eggs with creamy yolks and no gray-green ring around them.
Once cooled, gently peel the eggs under cool running water, starting from the wider end where the air pocket makes it easier. Slice each egg lengthwise and carefully scoop the yolks into a small bowl, setting the white halves aside on a serving plate. I like to arrange the whites in rows as I go—it makes plating the finished eggs much faster at the end.
Add mayonnaise and mustard to the bowl with the egg yolks and mash together until smooth and creamy, breaking up any lumps in the yolks. Stir in the shredded cheddar cheese and most of the bacon bits (reserving a small amount for garnish). Season with a pinch of salt and pepper to taste. The bacon and cheese add savory depth to what would otherwise be a simple mayo-based filling, so don't skip them even though they seem like small amounts.
Spoon or pipe the yolk mixture evenly into the egg white halves. Top each with a small sprinkle of the reserved bacon bits and a light dusting of paprika for color and a hint of smoky flavor. Serve immediately or refrigerate until ready to serve—these are best enjoyed within a few hours of assembly.