Preheat oven to 375°F and lightly coat a 12-cup muffin tin with nonstick spray.
Halve peaches, peel if desired, and dice.
In a bowl, combine flours, baking soda, baking powder, salt, and cinnamon.
In a large bowl, whisk together sugar, egg, and oil until smooth. Stir in peaches.
Add half the flour mixture, stirring to incorporate. Stir in the cream, then add the rest of the flour mixture, stirring just until no dry bits remain, scraping the bottom as needed.
Divide batter between muffin cups and bake for 18-20 minutes, until golden. Let cool in the pan 5 minutes, then carefully transfer to a wire rack to cool completely.