Cook the pasta: Bring 6 quarts of salted water to a boil. Add the bucatini and cook until al dente, following package instructions. Reserve 1/2 cup of the cooking water, then drain the pasta.
Prepare the pancetta or bacon: Cut the pancetta or bacon into 1/4-inch chunks and set aside.
Sauté the garlic: Lightly smash three garlic cloves to split them, reserving one clove for later. Heat the olive oil in a medium sauté pan over medium-high heat. Add the smashed garlic cloves and cook until golden brown, then remove and discard them.
Cook the Pancetta or Bacon: Add the pancetta or bacon to the pan and cook until it begins to crisp around the edges. Stir in the wine and let it simmer for 1–2 minutes. Add the reserved garlic clove during the last 30 seconds, then remove the pan from the heat.
Mix the Eggs and Cheeses: In a small bowl, whisk together the eggs, Romano cheese, and Parmigiano-Reggiano until smooth.
Combine Pasta and Sauce: Return the pan with the pancetta to medium heat. Add half of the reserved pasta water, then toss in the cooked bucatini. Stir and cook briefly until the water reduces slightly. Remove the pan from heat.
Quickly pour in the egg and cheese mixture, stirring constantly to create a creamy sauce without scrambling the eggs. If the sauce is too thick, thin it with a bit more reserved pasta water.
Add Peas and Seasonings: Stir in the thawed peas and toss to combine. Season generously with black pepper and taste for salt; adjust if needed.
Garnish and Serve: Just before serving, toss in the chopped parsley. Divide the Carbonara into serving bowls and garnish with additional parsley. Serve immediately for the best flavor and texture.