1. Preheat your oven to 375 degrees Fahrenheit (190 degrees Celsius). Line a standard 12 cup muffin tin with paper liners.
2. In a large bowl, use a wooden spoon to mix the softened butter, vegetable oil, granulated sugar, and brown sugar until everything is well combined and smooth.
3. Add the eggs one at a time, beating well after each addition to incorporate them into the batter.
4. Stir in the baking powder, baking soda, ground nutmeg, ground cinnamon, salt, and vanilla extract. Mix these dry ingredients into the wet mixture until just blended.
5. Begin adding the flour and milk alternately, starting and ending with flour. First, fold in about one third of the flour using a rubber spatula. Mix gently until just combined. Next, pour in about half of the milk and stir just until combined. Add another third of the flour and mix gently. Then, add the remaining milk and stir until combined. Finally, add the last portion of the flour and mix until just incorporated. Be very careful not to overmix the batter at any stage. Overmixing will result in tough muffins that do not rise properly. Undermixing slightly is better than overmixing.
6. Spoon the batter evenly into the prepared muffin cups. Fill them quite full. Bake in the preheated oven for 17 to 19 minutes, or until the tops spring back when gently touched. Let the muffins cool in the pan for a few minutes before transferring them to a wire rack. Allow them to cool on the rack for at least 10 minutes before applying the glaze.

For the Glaze

1. While the muffins cool, prepare the glaze. In a medium bowl, whisk together the melted butter, powdered sugar, vanilla extract, and hot water until the mixture is smooth and has a pourable consistency.

Assembling and Baking

1. Once the muffins have cooled slightly on the wire rack, dip the top of each muffin into the prepared glaze. Let the excess glaze drip back into the bowl.
2. Place the glazed muffins back on the wire rack and let the first layer of glaze set and harden slightly.
3. For an extra layer of flavor and shine, dip each muffin top into the glaze a second time, allowing the excess to drip off. Let the glaze set completely before serving.