Step #1 In a bowl with an electric mixer cream the butter with the brown sugar until the mixture is light & fluffy & beat in the egg & the vanilla.
Step #2 Into the bowl sift together the flour, the baking powder, & the salt, beat the dough until it is firm enough to handle.
Step #3 Halve the dough & on a piece of wax paper form each half into a 6-inch log, using the wax paper as a guide.
Step #4 Chill the logs, wrapped in the wax paper, for at least 4 hrs or overnight.
Step #5 Preheat the oven to 350F.
Step #6 Cut the logs into 1/4-inch-thick slices with a sharp knife, arrange the slices 3 inches apart on lightly buttered baking sheets, & press a pecan half onto each cookie.
Step #7 Bake the cookies in batches in the middle of the oven for 10 to 12 mins, or until they are golden, & let them cool on the baking sheets for 1 min.
Step #8 Transfer the cookies to racks & let them cool completely.