Sift together the flour, baking powder, and baking soda; set aside.
Cream the butter and sugars until light and fluffy. Beat in the egg and vanilla. Gradually add the flour mixture, a bit at a time, until thoroughly blended. Stir in the chopped pecans.
Shape the dough into an even cylinder approximately 1 1/2 inches in diameter. Wrap in plastic wrap and chill for at least 15 minutes.
Preheat the oven to 350 degrees. Line a baking sheet with parchment paper or lightly butter it.
Remove the plastic wrap and cut the dough into slices approximately 1/4 inch thick. Place the slices on the baking sheet (leave room for them to spread) and lightly press a pecan half into the center of each. Bake until lightly browned, about 10-12 minutes. Let cool.