1. Cook angel hair pasta in a large pot of boiling salted water, stirring occasionally, until 2 minutes shy of al dente; about 12 minutes. Drain.
2. Transfer pasta to a large high-sided skillet or a Dutch oven, add 1/4 cup water, and set over medium-low heat. Stir in lemon zest, butter, and pepper. Increase heat to medium and cook, tossing with tongs and adding a little more water if pasta seems dry, until butter is melted. Add lemon juice, Parmigiano-Reggiano cheese, and salt and cook, tossing, until sauce thickens slightly and only a little liquid remains and pasta is al dente (increase heat to high if needed). Taste pasta and season with more salt if desired.
3. Divide pasta among plates or shallow bowls. Drizzle with extra-virgin olive oil and top with more Parmigiano-Reggiano cheese, if desired.