1. Preheat the oven to 425 degrees, and position the oven rack in the center. Spray a standard sized muffin tin with nonstick spray. I like to use Pam for Baking. Muffin liners can also be used.
2. In the bowl of an electric mixer, cream butter, oil and sugars on medium speed until smooth.
3. Add eggs one at a time, mixing until incorporated. Add vanilla extract and mix.
4. In a separate bowl, combine flour baking soda, baking powder, pumpkin pie spice, and salt. Stir the flour into the batter gradually, alternating between the flour mixture and the milk, starting and ending with the flour. Mix on low speed until well combined.
5. Use a scoop or two large spoons to fill each well with the batter until they are nearly full.
6. Bake for 15 minutes, or until the tops are light golden brown, and a toothpick inserted into the center comes out clean. Try not to over bake.
7. When the muffins are cool enough to handle, remove them from the muffin tin and place them on a cooling rack.

For the Glaze

1. Add the powdered sugar, melted butter, heavy cream, and maple extract to a small bowl and whisk together. Add tiny amounts of water, until you have a nice thick glaze. The consistency you want is just slightly thinner than toothpaste, so that when the whisk is lifted out of the glaze it falls back into the bowl in a slow thick ribbon. When the muffins are mostly cool, dip the top into the glaze and place them back on a cooling rack (with a paper towel underneath to catch drips). The glaze will be dry to the touch within about 10 minutes.