Butter an 8- or 9-inch square baking dish.

Stir together brown sugar and evaporated milk in a large, heavy saucepan. Bring to a boil over medium-high heat. Cook until temperature reaches between 234 and 240 degrees F (112 to 116 degrees C) or until a small amount of syrup dropped into cold water forms a soft ball that flattens when removed from the water and placed on a flat surface.

Remove from heat and stir in walnuts, butter, and vanilla. Continue to beat with a sturdy spoon until mixture loses its gloss. Pour into the prepared pan. Score into squares with a knife, then set aside until firm, about 5 minutes.

Cut into squares. Store in an airtight container in the refrigerator.