Fill a large pot with water and bring to a boil.
Add the pasta, followed by a handful of salt and stir. Cook pasta until al dente, stirring frequently, 5 to 7 minutes.
Drain, reserving 1/2 cup pasta water, set aside until ready to use.
Place a large skillet over medium-high heat and melt butter and oil together.
Add shallots and garlic and sauté for 2 to 3 minutes. Add olives and continue to sauté for 3 to 4 minutes. Deglaze the pan with the lemon juice and pasta water and simmer until ⅔ of the liquid has evaporated.
Add the pasta and toss mixture together. Sprinkle with grated Parmesan and continue to toss together until well combined. Lightly season with salt and pepper. Top with freshly shaved Parmesan and finish with lemon zest. Serve.