Bring a large pot of water to a boil and salt it. Add the pasta and cook to al dente.
While the pasta cooks, rub the inside of a saucepot with the cut side of the garlic, then heat the pot over medium heat. Melt the butter, whisk in the flour and cook for 1 minute. Whisk in the milk and cook to thicken, a couple of minutes.
Season the sauce with salt, pepper and nutmeg. Using a wooden spoon, stir the cheese into the sauce in a figure-eight motion to melt. Stir in the mustard and thyme, then remove from the heat.
Drain the pasta and toss it back into the hot pot. Pour the cheese sauce over the pasta and toss to combine. Adjust the seasonings, to taste, and serve in shallow bowls with a little thyme sprinkled on top for garnish.