Preheat oven to 325 degrees. Grease a large bundt cake pan well (about 10" in size).
With a standing mixer or hand mixer, cream butter until light and fluffy, about 1-2 minutes. Add in brown sugar and granulated sugar. Cream until well combined, about 1 minute.
Add in the eggs, one at a time, beating well after each addition (and scraping down the sides of the bowl as necessary).
In a separate bowl, sift flour, salt, baking soda, and cinnamon together.
Beginning and ending with the flour mixture, alternately add in flour and sour cream (I did it in thirds: 1/3 flour mixture, 6 Tbsp of sour cream, 1/3 flour mixture, 6 Tbsp of sour cream, and the last 1/3 of the flour mixture). Mix until just combined.
Stir in vanilla extract, and the fold in the fresh peaches.
Pour the batter into the prepared bundt cake pan, spreading the batter in an even layer.
Bake for 65-70 minutes, or until a cake tester comes out clean.
Allow to cool at least 10-15 minutes before removing from the pan.