Preheat oven to 350°F (180°C).

On a rimmed baking sheet, spread flour.

Bake for 5 to 7 minutes, checking every 2 minutes for any signs of burning. Let cool completely on pan.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, brown sugar, and salt at medium speed until fluffy, 3 to 4 minutes. With mixer on medium-low speed, gradually add toasted flour alternately with milk and vanilla, beginning and ending with toasted flour, beating just until combined after each addition. Gently stir in chocolate. Refrigerate until firm, about 20 minutes, if desired.