Preheat the oven to 400° F. Line a 12-cup muffin pan with paper liners or spray with cooking spray.
Combine the oats and milk in a large microwave-safe bowl. Microwave on high about 3 minutes until the oats are creamy and tender; set aside.
In a separate large bowl, whisk together the flour, cornmeal, wheat bran, baking powder, and salt.
Stir the honey, oil, 1 tablespoon lime zest, and egg, to the oat mixture, then add to the dry ingredients. Beat just until moistened; batter will be lumpy.
Gently fold in the raspberries.
Spoon the batter into the muffin tin, filling each cup about 2/3 full. Bake 16 to 18 minutes until the tops are golden brown and a toothpick inserted into the center of a muffin comes out clean.
Transfer the muffins to a wire rack to cool completely before serving.