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Place all the topping ingredients in a medium bowl and mix well to make a dense, smooth dough; set aside.
To make the cake batter, cream the butter and granulated sugar in a large bowl with an electric mixer until smooth. Add the sour cream, eggs, and vanilla and beat well. Place the flour, baking soda, and baking powder in a small bowl, stirring to combine; add to the batter all at once, stirring well to combine. The batter will be stiff.
Smooth the batter into the prepared skillet. Arrange the peach slices on top in a single layer. Crumble the topping mixture into big chunks and sprinkle on top of the peaches.
Bake until a toothpick inserted in the center comes out with crumbs clinging to it, about 45 minutes. (The cake will remain quite moist because of the peaches, but be sure you don't have streaks of raw batter on the toothpick.) Cool a little before cutting into wedges.