Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, stirring occasionally, about 7-10 minutes. Reserve 1 cup of pasta water, then drain and set aside.
Heat a large skillet over medium heat. Add the chopped bacon and cook, stirring occasionally, until golden and crispy, about 8 minutes. With a slotted spoon, transfer the bacon to a paper towel-lined plate to drain. Carefully pour off all but 1–2 tablespoons of bacon fat from the skillet.
Add the frozen peas to the skillet with the reserved bacon fat. Cook and stir until heated through, about 3-4 minutes.
Return the cooked bacon to the skillet with the peas. Add the drained pasta and half of the reserved pasta water. Toss well over medium heat for 1–2 minutes until combined and hot.
Remove from heat and sprinkle the grated Parmesan cheese over the pasta. Toss thoroughly until the cheese melts and forms a light sauce. Add more reserved pasta water as needed to reach a creamy consistency.
Season with salt and pepper to taste. Serve immediately with extra Parmesan, if desired.