Preheat the oven to 350 degrees. Spray muffin pan with non-stick spray.
In a large bowl, combine the cornmeal, brown rice flour, baking powder, baking soda, salt, and rosemary. Whisk until combined.
Next, add the eggs, milk, and honey to the dry ingredients, and whisk until evenly combined.
Fill the muffin tins 3/4 full and bake for 15-18 minutes, until a toothpick inserted into the center of the cornbread comes out clean.
Remove from oven and let cool in the pan for 5 minutes, then transfer the muffins to a wire rack to finish cooling.