Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone liners.
Whisk together the flour, baking powder, and salt. Stir in the oats. Set aside.
Using an electric mixer on medium speed, beat the butter and brown sugar until thoroughly combined. Mix in the apple butter. Add the egg and vanilla, and mix well.
Reduce mixer speed to low. Gradually add the flour mixture, mixing just until combined. Stir in the nuts.
Drop the dough by tablespoonfuls onto the prepared pans, leaving about 2 inches between cookies. A cookie scoop works well for consistent portioning.
Bake 10 to 12 minutes, or until the centers appear set.
Cool on the pans for 5 minutes. Then transfer the cookies to a wire rack to cool completely.