Fill a large pot or Dutch oven with 4 quarts of water. Bring to a boil over medium-high heat. Stir in the salt. Add the pasta. Cook until almost tender (Taste a piece of pasta - the texture should be slightly firm, normally a minute less than the package instruction). Reserve 2 cups of the pasta water and drain the pasta.
Heat a large pan to medium heat. Add the olive oil or butter and swirl the pan. Add the sliced garlic and cook for 30 sec-1 minute on very low heat without browning. (If you prefer you can remove the garlic, the oil is well flavored) Stir in the pepper. Cook for 30 seconds, stirring constantly.
Keeping the heat down on low. Carefully add 1½ cups of the pasta water and bring to a simmer. Add the drained pasta and toss with tongs to coat with garlicky oil or butter. Sprinkle in 3/4 of the cheese, lemon juice and lemon zest.
Toss until well combined and the cheese melts into the sauce. Remove from the heat. If the pasta becomes dry, add more reserved pasta water.
Serve immediately topped with arugula, additional cheese and pepper, as desired.