In a heavy-bottomed 6 cup saucepan over medium-low heat, melt 2 tablespoons butter.
Add the flour and whisk together until the butter and flour mixture has small bubbles but does not brown, about 2 minutes.
Whisk in 1 cup of the stock all at once, and continue to whisk until it is smooth and lump-free.
Gradually whisk in the remaining 1 cup of stock, salt, and pepper.
Over medium heat, bring the sauce to a low boil, stirring constantly with a whisk.
Once the sauce reaches a low boil, keep whisking the sauce for 2 minutes.
Use immediately or pour into a storage container.
Spread the remaining 1 teaspoon of butter over the surface of the hot sauce to keep a skin from forming.
Cool the sauce for 10 to 15 minutes before refrigerating or freezing, covered with a lid.
