Preheat the oven to 350 degrees F (175 degrees C). Mix flour, baking soda, and baking powder together.

Mix peanut butter with 1/2 cup plus 1 tablespoon applesauce. Add sugar and salt. Mix well. Combine the flour and peanut butter mixtures together and stir well. Drop spoonfuls of dough 2 inches apart onto baking sheets.

Bake in the preheated oven until edges are golden but centers are still soft, 8 to 9 minutes.