Peel, core, and cut 4 apples into 24 (1/4-inch-thick) rings. Sauté apple rings, in batches, in a lightly greased skillet over medium heat 1 to 2 minutes on each side or until lightly browned. Remove from skillet, and place 1 apple ring in the bottom of each of 24 lightly greased muffin pan cups. Peel and finely chop enough remaining apples to equal 3 cups. Set aside. Stir together sugar and next 3 ingredients in a large bowl. Mix flour and next 3 ingredients; add to sugar mixture, stirring just until blended. (Batter will be stiff.) Fold in finely chopped apples and 1 cup pecans.
Spoon batter evenly over apple rings in muffin pan cups, filling cups three-quarters full.
Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Remove muffins from pan, and cool, apple rings up, on a wire rack.
Press the handle of a wooden spoon gently into the center of each apple ring, forming a 1-inch-deep indentation in the muffins. Spoon warm Quick Caramel Frosting evenly over muffins, filling indentations. Sprinkle evenly with remaining 1 1/2 cups chopped pecans.