Bring a pot of water to a boil. Carefully lower in the eggs and cook for 10 minutes. Transfer immediately to an ice bath and let cool completely before peeling.

Slice the eggs in half lengthwise and remove the yolks to a bowl. Set the whites aside.

Add the diced guanciale to a cold pan and place over medium heat. Cook, stirring occasionally, until the fat has rendered and the guanciale is crisp, about 6 to 8 minutes. Transfer to a paper towel-lined plate and reserve 1 1/2 teaspoons of the rendered fat.

Preheat the oven to 400–425°F. Line a tray with parchment paper. Add small mounds of finely grated Parmigiano and gently flatten into thin circles. Bake for 5 to 7 minutes, until melted and golden. Let cool completely, then break into shards.

To the bowl with the yolks, add the Parmigiano, reserved guanciale fat, lemon juice, mayonnaise, and several grinds of black pepper. Mash until smooth and creamy. Adjust with a touch more mayonnaise if needed.

Spoon or pipe the filling back into the egg whites, dividing evenly. Refrigerate until ready to serve.

Just before serving, top each egg with crispy guanciale, a shard of Parmigiano crisp, and additional freshly cracked black pepper.