In a medium saucepan, whisk together ¼ cup of the whole milk and the all-purpose flour until smooth.

Pour in the remaining ¾ cup of milk and add the kosher salt. Bring the mixture to a boil over medium heat, stirring frequently to prevent lumps.

Once the mixture reaches a boil, reduce the heat to low. Simmer for about 2 minutes, stirring constantly until the mixture starts to thicken.

Remove the saucepan from the heat. Stir in the shredded sharp cheddar cheese and freshly ground black pepper until the cheese is fully melted and the sauce is smooth.