You can use any cheese you desire. This recipe is really about the Bon Appetit technique of making it.
Theses are the step by steps from Bon Appetit Magazine
Add 3 big handfuls of kosher salt to a large pot of water and bring to a boil. (Salting your pasta water generously is the key to well-seasoned pasta.) Drop the pasta into boiling water and give them a good stir to be sure nothing sticks. Set a timer according to package directions for al dente.
Cut 1 stick chilled unsalted butter into 8 pieces.
While pasta is cooking, heat 2 Tbsp. butter and 2 tsp. freshly ground pepper in a large heavy pot or Dutch oven over medium, stirring occasionally, until butter is melted and foaming, but not browned, and pepper is fragrant, about 1 minute.
Add 1 cup whole milk to butter to stop it from browning and bring to a simmer. Whisk remaining 6 Tbsp. butter into milk mixture 1 Tbsp. at a time, allowing each to fully melt before adding the next. (Doing this gradually is important—it helps to emulsify your sauce.) You may need to adjust your heat occasionally to maintain a simmer. If pasta still needs a few more minutes to cook, turn off heat under your sauce, cover pot, and keep warm.
Scoop up 2 cups pasta cooking liquid with a large glass measuring cup. You're probably not going to use all of the pasta water in your sauce, but it's better to have more than you'll need.
Drain pasta and add to pot with milk mixture. Return to medium heat and cook, tossing with a wooden spoon to evenly coat all shells, about 30 seconds.
Add about one-third of grated cheese, stirring pasta vigorously with wooden spoon to melt. Add about ½ cup reserved pasta water and continue to stir until combined. Repeat this process 2 more times with remaining cheese. You may not need all of the pasta water, so add ½ cup at a time until pasta is very creamy and well coated. It’s always good to err on the side of looser (with a little extra pasta water) because the sauce will thicken as it cools. Give it a taste and add more salt, if needed.