For the muffins:
1/4 cup butter, room temperature
1/4 cup vegetable oil
1/2 cup granulated sugar
1/3 cup golden brown sugar, packed
2 large eggs
1-1/2 teaspoons baking powder
1/4 teaspoon baking soda
1 teaspoon cinnamon
3/4 teaspoon ground nutmeg
3/4 teaspoon table salt
1 teaspoon vanilla extract
2-2/3 cups all-purpose flour
1 cup milk

For the Glaze:
3 Tablespoons butter, melted
1 cup confectioners' sugar, sifted
3/4 teaspoon vanilla
2 Tablespoons hot water