Bring a large pot of water to a boil for the pasta and salt it. Add the pasta and cook to al dente. Heads up: you'll need to use a ladle of the cooking water (about 1/4 cup) for the sauce right before you drain the pasta.
Place a larage skillet over low heat with the butter, 1 tablespoon of the EVOO, and pepper. Let it hang out until the pasta is done.
When the pasta is ready, take a ladle of the starchy cooking water and add it to the butter-pepper mixture. Drain the pasta and toss it in the pan with the sauce. Turn off the heat. Add the cheese in small handfuls, then toss the pasta with tongs, until all the cheese is incorporated into the creamy sauce. Add another ladle of cooking water if needed, then season the pasta to taste with salt and drizzle with 2 tablespoons of the EVOO.
While the pasta works, defrost the spinach in the microwave for 6 minutes on high. Place the spinach in a clean kitchen towel and wring the water out. Heat a small skillet over medium heat. Add the remaining 2 tablespoons of EVOO, twice around the pan, then the garlic. Cook the garlic for 2 minutes, and then add the beans. Add the spinach to the beans, breaking it tup as you drop it into the pan. Season the spinach and beans with nutmeg, salt, and pepper. Serve the spinach and beans alongside the hot pasta.