Spray counter lightly with nonstick cooking spray. Combine 8 dinner rolls into a ball and roll into a 6-by-16-inch rectangle. Repeat with remaining rolls. Cover with plastic wrap and let rest.
In a large bowl combine apples, caramels, brown sugar, 1/2 cup almonds, cinnamon and flour. Remove wrap from dough. Divide apple mixture equally between the two rectangles and spread down the center of each rectangle.
Fold both edges of each rectangle over the filling, overlapping slightly, and pinching together to seal. Place both filled rectangles on a sprayed baking sheet and carefully braid them together. Press ends together. Cover with sprayed plastic wrap and let rise 15-20 minutes.
Remove wrap and bake at 350 degrees for 25-30 minutes or until lightly browned. Cool slightly. Microwave vanilla icing for 10 seconds. Drizzle over twist and sprinkle with remaining 1/4 cup almonds.