Cook the elbow macaroni in boiling salted water as per the package instructions.
While the macaroni is cooking, melt the butter in a pot (I use a 3 to 4-quart pot) over medium-low heat.
When the butter has melted, add the flour, ½ teaspoon salt, and ⅛ teaspoon black pepper. Cook, stirring constantly, for 1 minute. Don't let it get too brown. It should stay a nice light golden color.
Slowly add the milk while stirring constantly.
Increase the heat and bring the mixture to a boil, stirring frequently; then reduce the heat and simmer, stirring frequently, until the sauce has thickened, about 2 to 3 minutes.
Turn off the heat and add the cheese; stir until the cheese has melted completely.
Drain the cooked macaroni and add it to the cheese sauce; stir until the macaroni is evenly coated with the sauce.
Taste and adjust seasoning as needed; serve immediately.