For Sticky Buns: Scald milk in medium saucepan. Remove from heat. Add butter, granulated sugar and salt. Mix until butter is melted. Cool to 90ºF. Stir in egg, vanilla and yeast. Let stand 5 min.
Pour milk mixture into electric mixer bowl fitted with dough hook. Add flour. Mix on low speed until a dough forms. Mix on medium speed 7 min. or until a smooth, uniform dough forms. Transfer dough to lightly oiled bowl, cover, and let rise until doubled in volume. (Prepare Sticky Filling while dough is rising.)
Press dough down lightly and transfer to lightly floured surface. Roll out to 18x10-inches. Cover surface of dough with brown sugar and cookie pieces. Brush water along the top 1 inch edge of the long side of dough. Roll up from the long edge. Cut into 14 equal pieces and arrange cut-side up in muffin pan prepared with Sticky Filling. Cover and let rise until doubled in size.
For Sticky Filling: Melt butter in heavy saucepan on medium heat. Add remaining ingredients, except cookie pieces; mix until smooth.
Portion 0.6 oz. mixture into bottom of each of 14 large muffin cups. Top with 0.3 oz. cookies pieces. Set aside until ready to fill with dough and bake.
Bake in 350ºF standard oven 25 min. Remove pan from oven and immediately invert onto parchment paper-lined sheet pan. Immediately sprinkle buns with remaining 4.25 oz. cookie pieces. Serve warm.