In the bowl of your stand mixer fitted with a dough hook, whisk together sugar, warm milk, and yeast. Let sit for 5 minutes.
¼ cup granulated sugar, 1 ¼ cups warm milk, 1 packet active dry yeast
Add egg, melted butter, salt, and flour. Mix on low speed until combined, then increase speed to medium and mix until the dough pulls away from the sides of the bowl, about 2 minutes.
1 large egg, ¼ cup salted butter, ¼ teaspoon salt, 4 ½ cups sifted all purpose flour
Continue to mix the dough in the mixer for another 5-10 minutes.
Lightly grease a clean bowl with nonstick cooking spray. Place the dough in the bowl and cover with a clean towel.
Let dough rise for about 1 ½- 2 hours, or until doubled in size.
Grease a large bundt pan with nonstick spray.
For the coating: In a shallow bowl, mix together the sugar and cinnamon.
½ cup granulated sugar, ½ tablespoon ground cinnamon
After the dough has risen, punch it down to release the air.
Working one at a time, shape a small amount of dough into about a 1-inch ball.
Roll each ball of dough into the cinnamon sugar mixture then place it into the prepared bundt pan until all dough is used.
Pour any remaining cinnamon sugar on top of the dough in the bundt pan.
Cover the pan with a clean kitchen towel and let the dough rest for 20 minutes.
Make sure your oven rack is on the lowest setting to prevent the top of the monkey bread from burning. Preheat oven to 350 degrees F.
For the sauce: Melt butter in a small sauce pan over low heat.
6 tablespoons salted butter
Whisk in brown sugar and vanilla extract until the sugar dissolves.
¾ cup light brown sugar, 1 teaspoon vanilla extract
Remove from heat and pour on top of the monkey bread in the bundt pan.
Bake for 35-45 minutes, or until golden brown on top. Cover loosely with foil during baking if the top starts to brown too quickly.
Cool for 10 minutes in the pan, then flip onto a large serving plate.
Make the icing: Add powdered sugar, milk, and vanilla to a small bowl. Whisk to combine.
1 cup powdered sugar, 1-2 tablespoons milk, ½ teaspoon vanilla extract
Pour over the top of the monkey bread.
Notes
Milk: You can use any milk you prefer, but whole milk will give you slightly richer, softer dough.
Yeast: You can substitute an equal amount of instant dry yeast.
Butter: If using unsalted butter, increase the salt to 1/2 teaspoon in the dough and add a small pinch of salt in the sauce.
Flour: Too much flour will give you dry, heavy dough. To properly measure it, either weigh it (click "metric" just above the ingredients for the weights) or sift the flour, lightly spoon it into the measuring cup, and level.