Preheat oven to 400 degrees F (200 degrees C). Grease muffin cups or line with paper muffin liners.
In a large bowl, mix together oats, buttermilk, brown sugar, applesauce, molasses and eggs. In a separate bowl, stir together flour, baking soda and baking powder. Stir flour mixture into eggs mixture, just until moistened. Fold in peaches. Spoon batter into prepared muffin cups.
Bake in preheated oven for 15 minutes. While muffins are baking, combine 2 tablespoons sugar and 1/2 teaspoon cinnamon. After 15 minutes of baking, remove muffins from oven and sprinkle with cinnamon sugar. Return to oven and continue baking for 3 minutes, until a toothpick inserted into center of a muffin comes out clean.