Combine the two flours, salt, and baking powder in a medium bowl and whisk to blend.
In a large bowl, whisk the eggs until blended, then add the granulated sugar and whisk until mixture thickens a bit. Add the brown sugar and whisk until it is dissolved.
Slowly whisk in the melted butter, followed by the sour cream, and then the vanilla and almond extracts.
Stir the flour mixture into the wet mixture until it is just combined.
Place large spoonfuls of batter over the peach slices. When all the batter is in the cake pan, carefully smooth it out. Tap the cake pan on a surface like the kitchen counter gently to help the batter settle evenly over the peaches.
Bake the cake for 30-35 minutes, or until it is golden brown on top and a toothpick inserted into the center comes out with just a few crumbs attached.
Remove to a cooling rack and allow to sit at room temperature for 20-25 minutes.
Run a table knife around the outside edges of the cake to make sure the sides are loosened from the pan. Place an inverted plate atop the cake pan then quickly turn the cake over. Lift the cake pan off.