Heat olive oil in a large skillet over medium heat. Add the sausage and cook until browned. Add the butter and diced onion. Sauté until the onion becomes soft and translucent, scraping up any flavorful browned bits from the bottom of the skillet.
Meanwhile, bring a large pot of salted water to a boil. Cook the pappardelle according to package directions. Reserve ¼ to ½ cup of the pasta cooking water, then drain the pasta.
Reduce the heat to medium-low. Add the peas to the sausage mixture and cook for 1 to 2 minutes.
Stir in the milk or half-and-half, reserved pasta water, and Parmesan cheese. Simmer gently until the cheese melts and the sauce becomes creamy.
Add the lemon juice and stir to combine. Add the cooked pappardelle and toss until the pasta is fully coated in the sauce.
Season with salt and freshly ground black pepper to taste. Garnish with chopped Italian parsley and serve immediately.