Preheat oven to 350°.
Combine flour, baking powder, and salt in a small bowl; set aside. Beat sugar and butter at medium speed of a mixer until light and fluffy. Add vanilla and egg; beat well. Add flour mixture; beat at low speed until well blended. Shape dough into a ball, and wrap in plastic wrap; freeze 15 minutes. Divide dough into 16 equal portions. Gently press each dough portion into bottom and up sides of 16 (1 3/4 inch) miniature muffin cups coated with cooking spray; set aside.
Melt butter in a large skillet over medium-high heat; add apple. Cook apple, stirring frequently, over medium-high heat 2 minutes. Add caramel and remaining 5 ingredients; mix well. Spoon filling evenly into shells. Bake at 350° for 22 minutes. Let cool in pans on wire racks. Loosen tartlets from sides of pans, using a knife or narrow metal spatula. Remove from pans; let cool completely on wire racks.