1. Preheat oven to 350 degrees F. Combine flour, oats, baking powder, and salt in a small bowl.
2. In a large bowl, blend peanut butter, butter, and vanilla with an electric mixer. Add white and brown sugar, half of the flour mixture, and the beaten egg, blending after each addition. Finish with the remaining flour mixture and pecans.
3. Roll dough into 24 balls, about 1 rounded tablespoon each. Arrange balls about 2 inches apart on nonstick baking sheets. Using a fork, flatten dough balls, forming a crosshatch design on the tops.
4. Bake for 20 minutes. Let cool for 5 minutes in pans, then transfer to racks and cool completely.