1Heat oven to 350°F (325°F for dark or nonstick pans). Generously grease bottom and sides of two 9-inch round pans or spray with baking spray with flour. (Do not use 8-inch rounds or batter will overflow.)
2Beat cake mix, pudding mix (dry), water, butter and eggs in large bowl with electric mixer on low speed 30 seconds; beat on medium speed 2 minutes. Toss 1/2 cup of the brickle chips with flour in small bowl; stir into cake batter (batter will be thick). Spoon evenly into pans.
3Bake 30 to 35 minutes or until toothpick inserted in center comes out clean. Cool 10 minutes. Run knife around side of pans to loosen cakes; remove from pans to wire rack. Cool completely, about 1 hour.
4Beat whipping cream and brown sugar in chilled large bowl with electric mixer on high speed until soft peaks form. Spread about 1/2 cup whipped cream mixture over 1 cake layer to within about 1/4 inch of edge; sprinkle with 1/2 cup of the brickle chips. Top with second layer. Frost side and top of cake with remaining whipped cream mixture. Press remaining 1 cup brickle chips into side of cake. Store covered in refrigerator.