Cut dinner rolls into thirds. Arrange half of the cut rolls into the bottom of the pan. Sprinkle half of the pudding mix over the rolls, and sprinkle with half of the walnuts. Then repeat.
Combine brown sugar and butter. Heat together until butter is melted and a syrup is formed (microwave about 1 1/2 minutes). Pour syrup over rolls.
Cover with sprayed plastic wrap. Let rise until double in size or even with top of bundt pan.
Carefully remove wrap. Bake at 350°F for 30-35 minutes. Cover with foil the last 15 minutes of baking.
Immediately after baking, loosen from sides of the pan with a knife and invert onto a serving plate.