In a small bowl, combine flour, baking powder, baking soda and salt; set aside. In 350 °F oven, toast 1 cup pecan halves, about 3 minutes; let cool. Pulse in food processor or blender with on-and-off movement until finely ground. Set mixture aside. In a large mixing bowl, cream together butter and sugar until light and fluffy; beat in eggs and vanilla extract. Gradually blend in flour mixture. Stir in pecan mixture. Cover dough; refrigerate 45 minutes. Preheat oven to 375 °F. Drop by rounded measuring tablespoonfuls about 3 inches apart onto lightly greased cookie sheets. Top with 3 pecan halves. Bake 10 to 12 minutes, until edges are lightly brown and center no longer look wet but are still very soft to the touch. (do not over-bake; cookies will firm up as they cool.) Cool 5 minute on cookie sheet. Remove cookies from sheet to wire rack; let cool completely. Store cookies in airtight containers, or wrap individually in plastic and seal in food-storage bags. Cookies will keep at room temperature 3 days; for longer storage, keep in freezer.