Cook the pasta according to the package directions until al dente. Drain and set aside.
Return pot to stove and melt butter, along with ½ cup milk, whisking frequently.
Meanwhile, place the remaining ½ cup of milk and flour in a small bowl and whisk together until there aren't any lumps.
When you just start to see wisps of steam rising from the warming milk, whisk in the milk-and-flour mixture. Continue whisking gently until the milk thickens slightly to the consistency of heavy cream (~ 3-4 minutes)
Season with a pinch of salt and a few grinds of black pepper.
Remove from heat and add grated cheese and pasta until combined. Stir until the pasta is evenly coated.