Preheat oven to 425°F.
Add butter, vegetable oil, sugar and brown sugar to the large bowl. Cream it using a wooden spoon until smooth. Add one egg at a time, mix together. Then, add baking powder, baking soda, ground nutmeg, cinnamon, salt and vanilla extract. Mix until combined.
Add 1 cup of flour. Using a spatula, stir until just combined.
Add half of the milk and stir until just combined.
Repeat steps 3 and 4. Then, add the remaining flour and mix until combined.
Line muffin pan with 12 muffin liners.
Spoon batter evenly into the prepared muffin cups. Fill them nearly full. Bake in the preheated oven for 15 minutes. Muffins should be golden and springy to the touch. Let them cool for 10 minutes. Then, remove the muffins from the pan and let them cook for another 10 minutes on the rack.
While the muffins are cooling, you can prepare the icing. In a bowl, whisk together melted butter, powdered sugar, vanilla extract and hot water.
Dip each muffin in the glaze. When the glaze has hardened, dip each muffin into the glaze one more time. Enjoy!