For the pasta: Cook the linguine in a large pot of boiling salted water until al dente. Drain and set aside.
For the alfredo sauce: Heat the butter in a large saucepan over medium-high heat. Saute the garlic in the butter until golden and fragrant, 1 minute. Deglaze the saucepan with the chardonnay, and cook off the liquid for a few minutes until it's almost dry. Add the half-and-half and reduce the heat to medium low. Stir often, making sure the half-and-half doesn't boil. If it looks like it's about to start boiling, take the pan off the heat for a few seconds and lower the temperature. Cook the half-and-half until slightly thickened, about 8 minutes.
Add the Parmigiano, and stir until the cheese has completely melted. Cook for another 3 to 5 minutes, until the sauce is thick, creamy and smooth. Again, be careful not to boil the sauce. Once the sauce is done, remove it from the heat, and mix in the minced parsley and sea salt and freshly ground pepper to taste.
Toss the linguine with the alfredo sauce. Garnish with more minced parsley. Serve immediately.