Preheat oven to 375° F and line muffin tin with paper liners or spray with nonstick cooking spray.
In large bowl, or bowl of stand mixer, cream together butter and both sugars. Add eggs, one at a time, mixing in between and scraping down sides of bowl as necessary. Add vanilla and vegetable oil and combine.
Stir in flour, baking powder, baking soda, salt, nutmeg, and cinnamon. Add milk and stir to combine.
Scoop mixture into prepared muffin pan, filling each 2/3 full. Bate at 375° F for 18-20 minutes or until toothpick inserted in center comes out clean. Remove from oven and let cool in tin for about 5 minutes then turn out onto cooling rack to cool completely.
While muffins are baking, add melted butter, powdered sugar and vanilla to small bowl and whisk to combine and "melt" the powdered sugar. Add water slowly until desired consistency is reached.
When muffins have cooled completely, dip top of muffin in glaze mixture, then turn right-side up to allow glaze to harden. Serve immediately.