Preheat the oven to 400 F. Line a 12-cup muffin pan with paper or foil liners.
In a large microwave-safe bowl, combine the oats and milk. Microwave on high until the oats are creamy and tender, about 3 minutes. Set aside.
In a large bowl, combine the flour, cornmeal, bran, baking powder and salt. Whisk to blend. Add the honey, canola oil, lime zest, oats mixture and egg. Beat just until moistened but still slightly lumpy. Gently fold in the raspberries.
Spoon the batter into the muffin cups, filling each cup about 2/3 full. Bake until the tops are golden brown and a toothpick inserted into the center of a muffin comes out clean, 16 to 18 minutes. Transfer the muffins to a wire rack and let cool completely.