Bring a large pot of water to a boil. Salt generously and cook fettuccine 1 minute less than package al dente time. Before draining, scoop out at least 1/2 cup of pasta cooking water and set aside.
While pasta cooks, melt butter in a wide 12-inch skillet over medium-low heat. Add minced garlic and stir continuously for 60 to 90 seconds until fragrant and softened with no browning.
Pour heavy cream into the skillet in a slow stream while stirring. Increase heat to medium and bring to a gentle simmer with small bubbles at the edges. Cook for 4 to 5 minutes, stirring every 30 seconds, until the cream coats the back of a spoon.
Remove the pan completely from the heat. Wait 30 seconds. Add freshly grated Parmesan in three separate batches, stirring steadily after each addition until fully melted before adding the next.
Return pan to very low heat. Stir in 2 tablespoons of reserved pasta water to adjust consistency. Add more water 1 tablespoon at a time until the sauce pours smoothly from a spoon. Season with salt, white pepper, and black pepper.
Drain pasta and add directly to the skillet. Use tongs to toss and fold the pasta through the sauce for 60 to 90 seconds over very low heat until each strand is evenly coated. Serve immediately.