Scones: Sift flours, baking powder and salt into bowl; set aside. Rub vanilla bean seeds into granulated sugar in separate bowl; set aside.
Cream butter with electric mixer fitted with paddle attachment on medium speed. Beat in vanilla sugar and vanilla until well combined. Add dry ingredients all at once, mixing until coarse crumbs form, scraping side of bowl once. Add cream all at once; mix just until blended. Do not over mix. Stir in cookie pieces just until combined.
Roll dough on lightly floured surface to a rough rectangle 5/8-inch thick. Square off edges. Cut dough into 2-inch wide horizontal strips. Starting at the bottom left edge of 1 strip, measure in 1-1/2 inches and make a diagonal cut that meets the top left edge to create the first side of the triangle (you may have a small piece of discarded dough.) Then, measure in 3 inches from the top left edge and make a second diagonal cut to create the first triangle. Continue making alternating diagonal cuts along the dough strip to create connected triangles with 3-inch bases.
Place scones on parchment paper-lined sheet pans. Bake in 400°F standard oven 13 to 15 min. or until lightly golden brown. Remove to wire racks to cool.
Icing: Whisk powdered sugar and milk until smooth. Dip top of each scone into icing. Place scones back on wire rack until icing is set.