Preheat oven to 350 degrees F. Lightly spray an 8x8-inch baking dish with nonstick cooking spray. Line the bottom and sides with a sheet of parchment paper, leaving an overhang on two opposite sides to make lifting the bars out easier after baking.
To make the crust, place the white whole wheat flour, coconut sugar, and salt in the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, you can make the crust in a food processor or mix by hand using a pastry blender or your fingertips.) Mix briefly to combine the dry ingredients. Add the cold butter cubes and mix on low speed until the butter is broken down into small pieces and the mixture looks sandy and crumbly. When you press some between your fingers, it should just begin to hold together.
Scoop out and reserve 1 cup of the crust mixture for the topping. Press the remaining mixture firmly and evenly into the bottom of the prepared pan to form a compact crust. Bake for 14–15 minutes, until lightly set but not browned.
While the crust is baking, prepare the peach filling. In a large bowl, whisk together the ¼ cup white whole wheat flour, egg, Greek yogurt, honey, vanilla extract, cinnamon, and salt until smooth and no lumps remain. Gently fold in the chopped fresh peaches, being careful not to mash them. Pour the filling mixture over the hot crust and spread it evenly.
Sprinkle the reserved 1 cup of crust mixture evenly over the top of the peach filling, breaking up any large clumps.
Return the pan to the oven and bake for 45–55 minutes, until the topping is golden and the peach filling is bubbling around the edges.
Let the bars cool completely in the pan on a wire rack, then refrigerate for at least 2 hours before slicing. For clean edges, run a sharp knife around the sides of the pan, then use the parchment overhang to lift the bars out onto a cutting board before cutting into squares.
Store leftover bars in an airtight container in the refrigerator.