Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt. Set aside.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg and vanilla extract until fully combined.
Gradually add the dry ingredients to the wet mixture, stirring just until combined.
Fold in the diced peaches, oats, and pecans if using, being careful not to overmix.
Drop rounded tablespoons of dough onto the prepared baking sheet, spacing about 2 inches apart.
Bake for 12-15 minutes, or until the edges are golden and the centers are set.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.