Preheat the oven to 425º. Prepare a 12 spot muffin tin by buttering each cup generously, or lining with papers.
In a large bowl, whisk together the cornmeal, flour, cornstarch, baking powder and soda, and salt - set aside.
In a smaller bowl, or a 4 cup measuring cup, whisk together the remaining ingredients: buttermilk, eggs, maple syrup and butter.
Pour the wet ingredients into the bowl with dry ingredients and fold together gently, taking care not to over-mix; you want a shaggy looking batter and a small dry spot here or there is fine.
Divide evenly in the prepared pan, filling each cup about 3/4 full.
Place the pan in the preheated oven for 10 minutes, reduce heat to 350, and bake about 7 more minutes, until a toothpick inserted in the center of a middle muffin comes out with just a few moist crumbs.
Remove the muffins to a cooling rack - you can serve them warm right away, or once cooled, wrap tightly to store at room temperature for a couple days. They can be reheated in a low oven for about 10 minutes.