Preheat the oven to 350°F. Spread the bran on a rimmed baking sheet and toast in the oven for about 10 minutes, stirring occasionally to prevent burning, until golden and aromatic. Transfer to a plate to cool.
Increase the oven temperature to 400°F. Lightly coat the muffin cups of a standard muffin pan with cooking spray or line with paper muffin cups.
In a medium bowl, soak the bran in the water until soft, 3 to 5 minutes. In a large bowl, combine the brown sugar, honey, oil, and egg, and stir until well mixed. Add the bran mixture and stir until combined.
In a medium bowl, whisk the flour, baking soda, and salt. Add the orange zest. Add the dry ingredients to the wet ingredients, stirring until combined. Stir in the raisins and cranberries. Spoon the batter into the prepared muffin cups, filling each about three-quarters full.
Bake for 15 to 20 minutes, rotating the pan after 8 minutes, until the muffins are golden brown and a cake tester comes out clean when inserted into the center of a muffin.
Let the muffins cool in the pans on a wire rack for 5 minutes and then transfer them to the wire rack to cool; don’t wait any longer or the steam released will cause them to start to collapse. These muffins keep well at room temperature if they’re wrapped well in plastic wrap or foil or stored in an airtight container, for up to 3 days.