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Preheat oven to 350F/175C degrees. Grease a 9-inch round or square pan. Set aside.
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To make the crumbs: In a medium bowl, mix together flour, brown sugar, and cinnamon. Add the melted butter and mix with a fork until the mixture is uniformly moistened and thick crumbs form. Crumble it with your hands to make some big chunks.
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To make the cake: In a medium bowl sift together flour, baking powder, baking soda and salt. Set aside.
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In a medium bowl using a mixer fitted with a paddle attachment, beat the butter and sugar on medium speed for about 3 minutes, until light and fluffy. Scrape down the sides and bottom of the bowl as necessary. Beat in the eggs, one at a time until combined. Beat in vanilla extract. On low speed, beat in the flour mixture in 3 additions, alternating it with the sour cream in 2 additions, starting and ending with the flour. Do not overmix.
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Scrape the batter into the prepared pan and smooth the top. Arrange the peach slices over the top of the batter in an even layer. Sprinkle the crumb mixture evenly on top of the peaches, pressing it down gently.
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Bake for 50-60 minutes, until a toothpick inserted into the center of the cake comes out clean. The cake will be moist because of the peaches, but make sure it's not raw. If the crumbs layer is getting too brown while baking, cover pan loosely with aluminum foil. Let cake cool completely on a wire rack.
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Store cake at room temperature in an airtight container for up to 3 days or refrigerate for up to 5 days.