Preheat oven to 350 degrees F (175 degrees C). Grease an 8x8-inch baking pan.

Whisk 1 1/3 cups flour and white sugar together in a bowl; cut in 1/2 cup butter with a pastry blender until mixture resembles coarse crumbs. Press flour mixture evenly into bottom of prepared pan.

Bake in the preheated oven until light golden, about 10 minutes; remove base from oven to cool slightly, leaving oven on, about 5 minutes. Sprinkle base evenly with raisins and walnuts.

Beat eggs well in a bowl with an electric mixer; beat in brown sugar until creamy, about 2 minutes. Beat 1/4 cup butter, vinegar, 1 tablespoon flour, and vanilla extract into sugar mixture just until combined; pour over base, covering raisins and nuts.

Bake in the preheated oven until bubbly, about 30 minutes. Allow to cool completely, about 30 minutes; cut into squares.