Preheat oven to 350°. Line two cookie sheets with parchment paper.

Dough In a medium bowl, whisk together flour, baking powder and salt and set aside. Using a mixer on medium speed, cream together sugar and shortening. Add egg and vanilla and combine well. Alternate adding flour mixture and milk, starting and ending with flour mixture. Make sure all ingredients are incorporated; dough will be soft. Divide dough into four even pieces, wrap in plastic wrap, and refrigerate at least 1 hour.

Filling In a large bowl, stir together chopped nuts and sugar. Add melted butter and stir until evenly moistened. Add egg whites and mix well until completely combined.

Assemble On floured surface, roll out a piece of dough into a rectangle, about 6x18 inches. Using an offset spatula, spread one-quarter of nut filling onto dough, leaving a small border around edge of dough. Roll up as a jelly roll, with short ends to left and right and seal ends.

Cut roll into 1-inch pieces and place on baking sheet cut-side-up. Repeat with remaining pieces of dough and filling (cookies should fit on two baking sheets.) Bake until cookies are a light golden, about 30 minutes. Transfer to wire rack and cool completely.

Ice the Cookies When cookies are cooled, whisk together powdered sugar, vanilla and milk in a small bowl. Dip tops of cookies into icing and let any excess drip off. Allow icing to set before storing. The cookies can be stored in an airtight container at room temperature up to 2 weeks. These cookies also freeze well.