Bring a large pot of water to a boil for the pasta and salt it; add pasta and cook al dente; **you will use a ladle of the cooking water for the sauce right before you drain the pasta.
Place a large skillet over low heat with the butter, 1 tablespoon of olive oil, 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 pasta and toss it in the pan with the sauce; turn off the heat; add in 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 olive oil.
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 olive oil, then the garlic.
Cook garlic for 2 minutes, then add in the beans; add the spinach to the beans, breaking it up as you drop it into the pan.
Season with nutmeg, salt, and pepper; serve the spinach and beans alongside the hot pasta.