Tuile Batter: Combine softened butter, powdered sugar and flour in mixing bowl. Beat with paddle on electric mixer on medium speed until butter is in very fine pieces. Reduce speed to low and slowly add egg whites. Cream until smooth.
Making Tuiles: Preheat oven to 350°F. Place tuile template on silicone mat. Use large spatula to spread tuile batter across template, completely filling in each cavity. Continue spreading back and forth until each cavity is full and smooth, and all excess batter is removed from top of template. Carefully lift off template. Put silicone mat on baking sheet and bake for 6 minutes. Check cookies every minute or so to prevent burning. Remove cookies from oven when the edges are just starting to brown. Quickly release cookies with spatula and mold around a can or finished cake.
Assembly: Place desired dessert (approximately 3" in size) such as chocolate cake, brownie, mousse, etc on dessert plate. Put hardened tuile cookie around dessert or when tuile comes out of oven immediately wrap around finished dessert. Garnish with white and milk chocolate shavings and dusted cocoa powder if desired.