As the dough is rising, melt 2 tablespoons of butter in a saucepan. Add the apple slices and saute until soft, for about 5 minutes. Drain the apples and set aside to cool. In a small bowl, mix together brown sugar, chopped walnuts and cinnamon.
Grease and line a 9x13 inch baking dish with parchment paper. After dough has doubled in size, place it onto a lightly floured surface and begin to roll it into a 13x10 inch rectangle. Butter the dough with 2 tablespoons of softened butter and sprinkle with a half of the brown sugar mixture. Then spread the apples on top and sprinkle with the remaining brown sugar mixture. Roll the dough up tightly beginning at the short side and seal well by pinching edges of roll together.
Leftover rolls can be heated for a few seconds in the microwave before serving.