In medium bowl, mix filling ingredients. Set aside. In large bowl, mix 1 cup of the flour, 1/4 cup sugar, the salt and yeast.
In 2-qt saucepan, cook 1/2 cup applesauce, 1/4 cup butter and the milk over medium heat, stirring constantly, until very warm (120-130°F). Add warm mixture and egg to flour mixture; beat with electric mixer on low speed until moistened. Beat on medium speed 2 min. Stir in enough remaining flour to make dough easy to handle.
Place dough on lightly floured surface; gently roll in flour to coat. Knead about 5 min or until smooth and springy. Place in large greased bowl, turning dough to grease all sides. Cover and let rise in warm place 45-60 min or until double. (Dough is ready if indentation remains when touched.)
Grease bottom and sides of 13x9" pan with shortening. Mix brown sugar, 1/2 cup applesauce, 3 Tbsp melted butter and the walnuts in pan; spread evenly.
Gently push fist into dough to deflate. Roll dough into 15x12" rectangle. Spread 2 Tbsp softened butter over dough; sprinkle with filling. Tightly roll up rectangle, beginning at 15" side; pinch edge of dough into roll to seal. Stretch and shape until even. Cut roll into twelve 1" slices. Place slightly apart in pan. Cover and refrigerate at least 8 hr but no longer than 48 hr.
Before baking, let rolls stand at room temperature 30 min (rolls will not rise during this time). Heat oven to 400ºF. Bake 20-25 min or until golden brown. Cool in pan 1 min. Place heatproof serving platter or tray upside down onto pan; turn platter and pan over. Let stand about 1 min so caramel can drizzle over rolls; remove pan. Serve warm.