Beat 1 cup softened butter at medium speed with an electric mixer until creamy. Gradually add 3/4 cup powdered sugar, beating until smooth. Stir in pecans and vanilla extract until blended.
Stir together 2 cups flour, 1/4 tsp. baking powder, and 1/8 tsp. salt.
Gradually add flour mixture to butter mixture, beating at low speed until blended.
Shape shortbread dough into 2 (7-inch) logs. Wrap each log in wax paper, and chill 4 hours, or freeze logs in zip-top plastic freezer bags up to 1 month.
Preheat oven to 350°.
If frozen, let logs stand at room temperature 10 minutes. Cut each log into 24 slices. Place shortbread slices 1 inch apart on lightly greased or parchment paper-lined baking sheets.
Bake shortbread slices at 350° for 10 to 12 minutes or until edges of slices are golden.
Remove shortbread from baking sheets, and place on wire racks; let cool completely (about 20 minutes). Store in airtight containers.