Combine 2 quarts water and salt in a large pot; bring to a boil over high. Add pasta, gently stirring to submerge in water; cook, stirring occasionally, according to package directions for al dente.
While pasta is cooking, heat olive oil in a small skillet over medium-low. Add pepper; cook, stirring occasionally, until gently sizzling, about 1 minute. Transfer pepper mixture to a large bowl.
Reserve 1 ½ cups cooking water; drain pasta. Set both aside to cool slightly, about 3 minutes.
Stir cheeses into pepper mixture in bowl. Gradually whisk in about 1 cup of the cooking water until the cheeses are completely melted and mixture is creamy. Add drained pasta; toss vigorously to coat, adding remaining ½ cup cooking water as needed to create a glossy sauce that clings to the pasta. Serve topped with chopped bacon and additional grated pecorino Romano and cracked black pepper.
