1Preheat oven to 350 degrees F (175 degrees C). Grease and flour an 8-inch square baking dish.
2Combine butter and milk in a large saucepan over low heat; cook, stirring occasionally, until butter melts, 3 to 5 minutes. Remove saucepan from heat. Stir brown sugar and egg into the butter mixture.
3Sift flour into the butter mixture; stir. Add walnuts and vanilla extract; stir. Pour the mixture into the prepared pan.
4Bake in the preheated oven until a toothpick inserted into the center comes out clean, 20 to 25 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack. Cut into 2-inch squares to serve.
Footnotes
Cook's Note:
It usually just takes about 18 minutes in my oven for the sides to get golden brown and pull away from the pan, so start checking these about 16 minutes into the baking time. And these do taste just like Applebee's(R) Blondies!