Set large pot of generously salted water over high heat.
While waiting for water to boil, add butter and olive oil to a large pan over medium-low heat. When butter is melted, add garlic. You may want to turn the heat down—nothing ruins flavor like burnt, bitter garlic!
Once garlic is golden, add anchovy fillets and smash using a flat wooden spatula. Stir occasionally until mixture is more or less uniform. Think of this as a rustic sauce—no need to be perfectly smooth. Add the lemon juice and stir.
Lower heat, and while sauce continues to cook, add pasta to water, and cook until not quite yet al dente.
Here's a trick I learned from working at a culinary school: To fully coat every single noodle with sauce, finish pasta in the sauce pan, mixing continually to soak up all that saucy flavor. And because your sauce will get creamy with a little bit of that starchy pasta water, I ditch a colander altogether and use tongs (plus maybe a wooden spatula for support). Scoop pasta directly from the water into the sauce pan. Alternatively, you can strain pasta and reserve a half cup of pasta water, then add that to your sauce. But I'm all about less mess.
When the pasta is well coated and cooked to your liking, garnish with fresh ground pepper, a touch of lemon zest, and grated Parmesan.
Caitlin is a Paris-based writer and editor. She wrote about food and wine while living in Madrid after college, and had a brief career as a lawyer before moving back to Spain to work in restaurants and attend culinary courses at the Basque Culinary Center in San Sebastian. She has worked or staged at Septime in Paris, Mina and Nerua in Bilbao, and Bien Cuit in Brooklyn. In 2018, she and her husband launched a pop-up sandwich shop in Mallorca, Spain. Caitlin now lives in an ovenless apartment in the 9th arrondissement with her husband, Guillaume, and daughter, Mimi. Update: we have an oven now.