In a small saucepan over medium heat, melt 2 Tbsp butter.
Add 2 Tbsp flour and whisk continuously for about 1 minute until the mixture is smooth, combined, and lightly thickened.
Slowly pour in 1¼ cups whole milk, whisking constantly to prevent lumps.
Increase the heat slightly and continue whisking as the mixture comes to a gentle simmer. Cook until the sauce thickens enough to coat the back of a spoon, about 3–5 minutes.
Remove the saucepan from the heat.
Gradually add 8 oz shredded cheddar cheese, a handful at a time, whisking after each addition until the cheese is completely melted and smooth.
Stir in ½ tsp salt.
If the sauce is thicker than desired, whisk in a little additional milk, 1 tablespoon at a time, until it reaches your preferred consistency.