Preheat oven to 375ºF. Stir together flour, cranberries, baking powder, apple pie spice, salt, baking soda, and 3/4 cup of the granola in a large bowl. Whisk together applesauce, brown sugar, butter, eggs, and vanilla in a medium bowl. Add applesauce mixture to flour mixture, stirring until just combined.
Fit 1 parchment square into each of the lightly greased cups of a 12-cup muffin pan, pressing folds into paper as needed. Divide muffin batter evenly among prepared muffin cups in pan. Lightly press apple pieces into tops of batter, and sprinkle with remaining 1/4 cup granola. Bake in preheated oven until a wooden pick inserted in center comes out clean, 22 to 27 minutes. Cool in pans on wire racks 5 minutes. Remove from pans to wire racks, and cool completely (about 30 minutes). Drizzle with Sticky Maple-Caramel Sauce before serving, if desired.