Bring a large pot of salted water to a rolling boil.
In a large, heavy-bottom saucepan or skillet over medium heat, melt the butter. Add the garlic cloves and sauté, turning the cloves over occasionally, until the garlic is fragrant (about 3 minutes). Remove and discard the garlic.
Add the gum-free flour blend, whisk to combine and cook just until the mixture begins to simmer. You don’t want any browning, as this is a white sauce. Add the salt and pepper, and whisk to combine.
In a slow, steady stream and while whisking constantly, pour the stock into the pan. Continue to whisk occasionally and cook until the mixture just begins to thicken and the mixture coats the back of a spoon (about 6 minutes).
While the sauce is cooking, boil the pasta to an al dente texture according to the package directions. Drain the pasta.
While the pasta is boiling, add the milk and cream, and whisk until fully combined. These will thin the sauce, but continue to cook, whisking frequently, until the sauce reaches your preferred consistency.
Remove the pan from the heat, add the finely grated Parmesan cheese and whisk until the cheese melts. Add the pasta to the sauce, and use tongs to toss until fully coated. Serve immediately.