2Whisk 4 large eggs, 4 oz. Pecorino Romano or Parmesan, finely grated (about 2 cups), and 1 tsp. freshly ground pepper in a large heatproof bowl until smooth and consistent; set aside.
3Line a plate with a double layer of paper towels. Slice 8 oz. guanciale ¼” thick (about the thickness of thick-cut bacon), then into 1x½” rectangles, and add them to a large high-sided skillet along with 1 Tbsp. extra-virgin olive oil. Spread guanciale into a single layer, set pan over medium-low heat, and cook, stirring occasionally, until fat has rendered and guanciale is deeply browned in spots, 8–12 minutes. Using a slotted spoon, transfer guanciale to prepared plate.