Preheat oven to 325°F. Grease and flour a bundt pan thoroughly. Set aside.
In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
In a large mixing bowl, beat butter and granulated sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition.
Mix in sour cream and vanilla extract until smooth.
Gradually add dry ingredients to the wet mixture, mixing just until combined. Do not overmix.
In a separate bowl, toss sliced peaches with brown sugar and cinnamon.
Pour half of the batter into the prepared pan. Add a layer of peaches.
Add remaining batter, then top with remaining peaches.
Gently swirl with a knife to create a marbled effect.
Bake for 70 to 80 minutes or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.