Fill a large pot with water and bring to a boil. Add a handful of salt followed by the pasta. Boil pasta until al dente, 6 to 8 minutes, stirring occasionally. Drain pasta into a colander and set it aside until ready to use.
Place a large skillet over medium heat and melt butter and oil together.
Stir in squid ink until smooth. Add garlic and sauté for 2 to 3 minutes.
Add pasta to the skillet and toss together with the sauce. Lightly season with salt and pepper. Cook for 2 to 3 minutes or until pasta is completely coated.
Top pasta with lots of freshly shaved Parmesan and lemon zest, if using. Serve.