Bring a large pot of water to a boil and salt it. Add 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 butter, whisk in flour and cook 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-8 motion to melt. Stir in the mustard and thyme then remove from heat.
Drain the pasta and toss it back into the hot pot. Pour the cheese sauce over pasta and toss to combine. Adjust seasonings to taste and serve in shallow bowls with a little thyme sprinkled on top for garnish.