Preheat the oven to 400 degrees F. Grease 12 standard muffin-pan cups, or line cups with fluted paper liners.
In a large bowl, whisk together the flour, baking powder, baking soda, cinnamon and salt. Stir in the oats. In a medium bowl, mix the applesauce, milk, molasses, brown sugar, oil and egg with a fork until blended. Stir in the carrots and prunes. Add the applesauce mixture to the flour mixture and stir just until the flour is moistened (the batter will be lumpy).
Spoon the batter into the prepared muffin-pan cups (the muffin cups will be full). Bake until a toothpick inserted into the center of a muffin comes out clean, 23 to 25 minutes. Immediately remove the muffins from the pan. Serve the muffins warm, or cool on a wire rack to serve later.