Step 1

Bring a saucepan of water to a boil; reduce heat to medium-low and cook the sprouts for 10 minutes. Drain, rinse in cold water, and set aside.

Step 2

Melt the butter in a saucepan over medium heat and stir in the flour, salt, and pepper. Cook the mixture until it turns a slight tan color, about 1 minute; whisk in the milk. Bring to a simmer, whisking constantly, and cook until thickened, about 2 minutes. Stir in the processed cheese until the cheese has melted and the sauce is thick and smooth. Transfer the Brussels sprouts into the sauce, stirring to coat.