Warm the milk on low heat until little bubbles form at the edges; remove from heat.
Melt 2 Tbsp. unsalted butter in a heavy-bottomed saucepan over medium heat. Stir in 2 Tbsp. all-purpose flour and cook, stirring constantly, until the paste cooks and bubbles a bit, but don't let it brown, about 2 minutes.
Slowly add 1¼ cups whole milk, heated, whisking to incorporate. Bring it to a boil, stirring constantly, as sauce thickens. Add kosher salt and freshly ground black pepper to taste.
Reduce to low heat, and cook, stirring, 2–3 minutes more. Remove from the heat. Do ahead: To cool this sauce for later use, cover it with wax paper or pour a layer of milk over it to prevent a skin from forming. Refrigerate for up to 3 days.
VARIATION: Cheese Sauce: Stir in ½ cup grated cheddar cheese during the last 2 minutes of cooking, along with a pinch of cayenne pepper. If adding cheese, only stir in the same direction to prevent sauce breaking.