Generously butter a 12-inch cup muffin tin; set aside.
In a large bowl, mix flour, sugar, and salt together.
In a liquid measuring cup, combine warm milk and yeast. Stir until yeast is dissolved.
In a medium bowl, lightly beat egg.
To egg, add milk mixture, vegetable oil, vanilla extract, and stir.
Add milk/egg mixture to flour and mix well until smooth. Put the batter into prepared muffin tins, filling about halfway to two-thirds full. Let rest for 15 minutes.
In a small bowl, mix cinnamon, nutmeg, and brown sugar. Add butter with a fork and combine until top is crumbly.
Place an equal amount of topping in each muffin tin, spreading evenly. Press topping into the rested dough with fingers or use a spatula to incorporate.
Place muffin into a cold oven and heat oven to 350 degrees. Bake for 20 minutes. Muffins should be lightly browned around edges and will spring back when the centers are gently pressed.
Cool for 30 minutes before combining confectioners' sugar and milk in a small bowl. Drizzle onto the muffins.