Bring a large pot of water to a boil and add 1 teaspoon salt.
In a medium saucepan over medium heat, melt 6 tablespoons unsalted butter.
Add 1 clove minced garlic to the melted butter and cook until fragrant and lightly golden, about 30–60 seconds.
Remove the pan from heat and let cool 3–5 minutes, then whisk in 1½ cups room-temperature heavy cream until combined.
Return the pan to low heat and warm gently without boiling.
Add 6.4 ounces freshly grated Parmesan a little at a time, whisking constantly until the cheese melts and the sauce is smooth.
Taste and season the sauce with kosher salt, ground black pepper, and minced fresh thyme if using.
While the sauce is finishing, cook 16 ounces fettuccine in the boiling water until al dente according to package directions; reserve ½ cup pasta cooking water before draining.
Toss the drained pasta with the Alfredo sauce, adding reserved pasta water a little at a time to reach the desired consistency; serve immediately.