Bring a large pot of water to a boil. Season well with salt (it should taste like well-seasoned broth).
In a large skillet, melt two tablespoons of the butter and, when foamy, add the white parts of the scallion, plus a pinch of salt. When soft, add the package of frozen peas and, at the same time, drop the pasta into the boiling water.
Using a ladle, lift about a cup of the pasta water into the skillet with the peas and scallions. Lower to a simmer and let that cook for a bit. If the skillet gets dry, add more pasta water. You don't want the temperature so hot that the peas break apart, so be gentle here.
When the pasta is cooked al dente (one minute less than the package directions; best to taste here), lift it with a spider tool into the skillet with the peas. Add another ladleful of pasta water, turn up the heat, and stir all around, until the pasta is coated in the buttery scallion pea mixture and there's no more liquid at the bottom of the skillet.
Turn the heat off, add the remaining butter, lots of black pepper, the zest of the lemon (zest it directly over the pasta to catch the oils), a little lemon juice (to taste), and at least 1/2 cup of the Parmesan. Stir it all around and taste to adjust with more lemon, black pepper, and Parmesan.
Serve in pasta bowls and top with more Paremsan and pepper.