In a large bowl, whisk together cornmeal, flour, baking powder, baking soda, pumpkin pie spice, and salt.
In a medium bowl, whisk together maple syrup, eggs, pumpkin puree, vegetable oil, vanilla extract, and milk.
Make a well in the dry ingredients and then pour the liquid mixture into the center. Using a spatula, gently start folding the dry ingredients with the wet until a dough formed.
Remove the muffin pan from the oven and carefully place 1/4 teaspoon of unsalted butter into each of the muffin cups. Carefully swirl around so it coats the entire cup or use a pastry brush to brush the entire cup with the melted butter.
Using a large cookie scoop or ice cream scoop, divide the batter evenly amongst the cups, filling 3/4 of the cup full.
Bake for 20 minutes, or until a toothpick inserted into the center comes out clean.
Let sit for 5 minutes then remove muffins from muffin pan and place on a wire rack to cool completely.
While the muffins are cooling, stir together the ingredients for the maple butter in a small bowl then use when serving the muffins.