Bring a pot of well salted water to a boil. Cook the pasta to a minute or so shy of recommended cooking time.
Meanwhile, heat the oil in a large, 12” (30cm) skillet over medium high heat. Add the shrimp shells and sauté until they begin to get spotty brown, about 5 minutes. Remove and discard the shrimp shells. (See note 2 below).
Reduce the heat to medium and add 2 TBS (25g) of the butter to the now empty skillet. When the foam starts to subside add the garlic and pepper flakes. Cook for about 30 seconds or so until the garlic becomes fragrant. Be careful not to over do the garlic or it will take on a bitter, acrid taste.
Add the shrimp and season with a generous pinch of salt and a few grinds of pepper. Sauté for about a minute and a half until the shrimp begin to turn pink. Toss the shrimp and cook on the second side another minute.
By this time the pasta should be ready. (See note 3 below). Add it to the pan with the shrimp and toss to combine, stirring in 1/2 cup of pasta cooking water. Continue to cook, tossing and adding pasta water by 1/4 cup fulls until the pasta is fully cooked but still al dente, another 2-3 minutes. There should be 2-3 TBS of thick, viscous pasta water remaining in the bottom of the pan.
Off heat stir in the remaining butter, lemon zest, juice, the basil leaves and the parmesan cheese.
Serve on warm plates sprinkled with more parmesan cheese and a drizzle of extra virgin olive oil..