Preheat your oven to 350°F (175°C). Lightly grease or line an 8x8-inch baking pan with parchment paper for easy removal.
In a medium bowl, combine the rolled oats, all-purpose flour, baking soda, ground cinnamon, and salt. Whisk these together until evenly blended.
In a separate large bowl, use a hand mixer or stand mixer to cream the softened unsalted butter with the brown sugar and granulated sugar until light and fluffy, about 2-3 minutes.
Beat in the egg and vanilla extract until just combined, being careful not to overmix.
Gradually add the dry oat mixture to the wet ingredients, mixing on low speed until just incorporated. The batter will be thick and slightly crumbly.
Gently fold in the diced nectarines, peaches, and chopped nuts if using, taking care not to break up the fruit.
Spread the batter evenly into your prepared baking pan. Bake for 30-35 minutes or until the top is golden brown and a toothpick inserted into the center comes out mostly clean.
Allow the bars to cool completely in the pan on a wire rack before slicing into squares.