Bring a large pot of water to a rolling boil, add a generous pinch of salt, and cook the linguine until al dente according to package directions.
Reserve 1/2 cup of the pasta cooking water, then drain the pasta in a colander.
Return the hot drained linguine to the pot (off the heat) and add the butter, heavy cream, minced garlic, a pinch of salt, and black pepper.
Toss or stir constantly until the butter and some of the cheese melt and begin to form a creamy sauce.
Add grated Parmigiano-Reggiano and stir; then add reserved pasta water a few tablespoons at a time (about 3 tablespoons used typically) until you reach your desired sauce consistency.
Taste and adjust seasoning with more salt and pepper if needed, then transfer to a serving platter and sprinkle with chopped fresh parsley and extra grated cheese if desired.
