Make the brown butter. In a small saucepan over medium heat, melt the butter, stirring occasionally. Continue to cook the butter until it becomes foamy and you can hear cracking and popping noises. Once that happens, continue to stir occasionally for 3-5 minutes until the butter develops a nutty aroma, brown bits start to form in the bottom of the pan and the butter turns an amber color. Once this happens, remove from the heat and pour into a mixing bowl. Allow to cool to room temperature, 20-30 minutes.
While cooling, preheat oven to 400°F. Spray a 12 count muffin pan with cooking spray or line with muffin liners and set aside.
In a large mixing bowl, whisk together the cornmeal, flour, baking powder, baking soda and salt. Set aside.
In another medium mixing bowl, whisk together the buttermilk, sugar, egg, maple syrup and cooled brown butter. Add the wet ingredients to the dry ingredients and mix gently with a wooden spoon, being careful not to overmix.
Scoop the batter into the prepared muffin tin until completely full, almost overflowing.
Bake for 15 to 18 minutes, until the tops are golden brown and a toothpick inserted in the center of the muffin comes out clean.
Cool in muffin pan for 10-15 minutes then transfer to wire rack to cool completely. Store in an air tight container for up to one week or in the freezer for up to 3 months.