Bring 4 quarts water to a boil in a large pot over high. Meanwhile, place pepper in a large heatproof bowl; set aside. Cook guanciale in a medium skillet over low, stirring often, until lightly browned, fat is mostly rendered, and guanciale feels crisp with a bouncy texture when squeezed, about 10 minutes.
Pour 3 tablespoons hot guanciale drippings over pepper in bowl; set guanciale aside.
Add egg yolks, eggs, and cheeses to pepper mixture; whisk until thoroughly blended, and set aside.
Add salt to water in pot; return to a boil over high. Add pasta; cook according to package directions for al dente, stirring occasionally. About 1 minute before pasta is finished cooking, scoop out 1/4 cup cooking liquid, and slowly pour into egg mixture, whisking constantly, until well combined and sauce is loosened.
Transfer about one-third of pasta to egg mixture using tongs, allowing excess liquid to drip off in pot; quickly and gently toss to combine. Transfer remaining pasta, allowing excess liquid to drip off in pot, to egg mixture.
Continue stirring and tossing the pasta with tongs until cheese is melted and sauce thickens slightly and coats pasta, about 1 minute. (The sauce will continue to thicken as it cools.)
Divide pasta evenly among 4 shallow serving bowls, and top with reserved crisped guanciale. Garnish with pepper and grated Pecorino Romano. Serve immediately.