In a large pot, bring 4 quarts water to a boil. Add the pasta and 1 tablespoon salt, then cook, stirring occasionally, until just shy of al dente. Reserve 1 cup of the pasta cooking water, then drain and return to the pot; set aside.
In a 12-inch skillet over medium-high, heat the oil until shimmering. Add the chicken, ½ teaspoon salt and ¼ teaspoon pepper; cook, stirring occasionally, until the chicken is golden brown all over, 7 to 9 minutes. Reduce to medium and add the butter and scallion whites. Cook, stirring only once or twice, until the butter smells nutty and the chicken is well browned, about 4 minutes. Add the lemon zest and reserved pasta water, scraping up any browned bits.
Scrape the chicken mixture onto the pasta in the pot. Cook over medium, stirring and tossing, until the pasta is al dente, 2 to 3 minutes. Off heat, stir in the lemon juice and parsley. Taste and season with salt. Serve sprinkled with pepper.
Optional garnish: Red pepper flakes OR finely grated pecorino Romano cheese OR both
