Bring a large pot of salty water to boil and thinly slice 3 garlic cloves. Drop the pasta and cook to al dente (about 2 minutes less than the package instructions).
While the pasta cooks, heat 3 tbsp olive oil in a large sauce pan on medium. Once hot, add sliced garlic and cook until softened and fragrant, about 2 minutes. Reduce heat to low, add anchovy fillets and press them into the oil using the back of a wooden spoon or spatula to press.
Add 1/2 cup pasta water and bring to a simmer. Cook until the sauce is slightly thickened, about 5 minutes. You'll know it's ready the gap created after passing your spoon through the sauce takes 5 seconds or longer to close.
By now the pasta should be ready. Reserve another cup of pasta water and drain the rest. Transfer the cooked pasta to the sauce pan and add in your cold butter along with 1/2 cup of the reserved pasta water. Stir until the butter is melted and a glossy sauce forms. You might need to add more pasta water as you go to get the right consistency. You’ll know it’s done when all the noodles are coated and the sauce is thick and creamy. Serve with lots of cracked black pepper and parmesan!
