Cook the pasta: Bring a large pot of salted water to a boil. Cook spaghetti until al dente, according to package instructions. Reserve 1 cup pasta water, then drain.
Crisp the pancetta: In a large skillet over medium heat, cook pancetta until golden and crisp (about 5–7 minutes). Remove from heat but leave the rendered fat in the pan.
Prepare the egg mixture: In a mixing bowl, whisk together eggs, egg yolks, and grated Pecorino Romano. Add a generous amount of freshly cracked black pepper.
Combine pasta and pancetta: Add hot, drained pasta to the skillet with pancetta. Toss to coat in rendered fat.
Create the carbonara sauce: Remove skillet from direct heat to prevent scrambling eggs. Pour in the egg-cheese mixture and quickly toss with tongs to coat pasta. Add reserved pasta water, a little at a time, until a silky sauce forms.
Serve: Divide into bowls. Top with extra Pecorino Romano and black pepper. Serve immediately.