In a large skillet combine olive oil and butter over medium heat. Add garlic, pepper and the lemon zest.
Salt water when it boils then cook cappellini to al dente, 2 to 3 minutes. Add a ladle of cooking water to lemon pepper butter and stir in the lemon juice. Drain pasta and toss with lemon-pepper butter and salt, to taste. Add the basil to the pasta and serve a small bundle alongside your entree or serve as a delicate first course.