Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch baking pan and line with parchment paper, leaving a 1-inch overhang on each side for easy removal.

In a medium bowl, whisk together the flour, pecans, granulated sugar, brown sugar, cinnamon, and salt. Incorporate the butter pieces using a fork until the mixture resembles coarse crumbs. Refrigerate until ready to use.

In a medium saucepan over medium heat, combine the peach slices, ½ cup brown sugar, cornstarch, and cinnamon. Cook, stirring occasionally, until the sugar dissolves and the mixture thickens into a syrupy consistency, about 6–8 minutes. Allow to cool.

In the bowl of a stand mixer fitted with the paddle attachment, cream the sugar, butter, vanilla, and salt until light and fluffy, about 4–5 minutes. Add the eggs, one at a time, beating well after each addition.

In a separate bowl, whisk together the flour and baking powder. In another bowl, whisk together the buttermilk and sour cream. Add the flour mixture to the creamed butter mixture in three parts, alternating with the buttermilk mixture, mixing on low speed until combined.

Spread two-thirds of the batter into the prepared pan. Sprinkle the remaining ½ cup brown sugar evenly over the batter. Spread the cooled peach filling on top, then cover with the remaining batter. Sprinkle the chilled pecan crumble evenly over the surface.

Bake for 70–80 minutes, rotating the pan halfway through. If the topping darkens too quickly, cover with foil after 60 minutes. The cake is done when golden at the edges and a toothpick inserted into the center comes out clean. Allow to cool on a wire rack for 30–40 minutes before slicing.