For the carbonara base sauce: Put the pancetta in a cold saute pan and then put it over medium-high heat. When the fat starts to melt, stir the pancetta once in a while so it doesn't burn in the pan. Allow the pancetta to cook in the rendered fat until crispy and brown, about 30 minutes. Remove the pancetta pieces to a plate lined with paper towels, saving the fat in the pan.
Whisk the flour into the pancetta fat to make a roux and cook for 2 to 3 minutes, stirring so it does not burn. Whisk the milk into the the roux. (Transfer to a large pot if your saute pan is not big enough to hold the sauce.) Allow the sauce to gently simmer for 15 minutes, stirring regularly. Whisk in the Parmesan and season with some salt and pepper. Simmer to melt the cheese, another 2 to 3 minutes. Hold warm for serving.
To finish the dish: Bring a large pot of salted water to a boil. Cook the pasta according to the package directions.
Meanwhile, season the shrimp with some salt and pepper. Heat a large saute pan over high heat until it begins to smoke. Add the oil and then, working in batches if necessary, cook the shrimp to get a golden brown sear, 2 to 3 minutes per side. You do not want to overcrowd the pan. Add more oil between batches if necessary. Squeeze the juice of 1 of the lemons over the shrimp, add the butter to the pan and remove from the heat to let the shrimp rest.
Bring the carbonara base sauce back up to a simmer. Add the pasta to the sauce and then add the peas and cooked pancetta. Adjust the consistency of the sauce with water if needed.
Add the shrimp to the pan with the pasta, toss and then season with some salt and pepper to taste. Add a squeeze of lemon juice from the remaining lemon.
To plate, divide the pasta and sauce among 6 bowls and arrange the pasta. Garnish with the parsley.
Optional: Top each dish with an egg yolk for stirring into the hot pasta to add richness to the sauce.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.