Place the shrimp on a sheet pan with 1 tablespoon olive oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Toss well, spread them in 1 layer, and roast for 6 to 8 minutes, just until they're pink and cooked through.
Meanwhile, drizzle some olive oil in a large pot of boiling salted water, add the angel hair, and cook al dente, about 3 minutes. Drain the pasta, reserving some of the cooking liquid. Quickly toss the angel hair with the melted butter, 1/4 cup olive oil, the lemon zest, lemon juice, 2 teaspoons salt, 1 teaspoon pepper and about 1/2 cup of the reserved cooking liquid. Add the shrimp and serve hot.