Special equipment: A Bundt pan
For the dough: Grease a large bowl with butter and set aside.
Pour the flour, sugar and salt into the bowl of stand mixer fitted with the dough hook.
Add in the yeast and turn on the lowest speed for 30 seconds to evenly distribute.
Add the milk, melted butter, eggs and 1/4 cup warm water (105 to 120 degrees F) to the flour mixture all at once. Beat on low- to medium-speed until the dough starts to pull away from the sides of the bowl.
Add in the sprinkles and mix until mostly distributed, about 30 more seconds.
Remove the dough from the mixer, shape it into a ball with your hands and place it in the greased bowl, turning once to coat the entire surface.
Spray a piece of plastic wrap with nonstick spray and cover the bowl. Let the dough rise until doubled in size. (You can also place in the refrigerator overnight.)
For the coating: Melt the butter in a medium microwave-safe bowl. Add in the granulated sugar and extracts and set aside.
Generously spray the bottom and sides of a Bundt pan. Preheat the oven to 350 degrees F.
Punch the dough down by pushing your fist into the center and then start pulling the edges into the center.
Pull apart the dough into small pieces about an inch across and roll in your hands to create smooth, uniform dough balls. Place one layer of dough balls into the Bundt pan, then pour a third of the melted butter mixture over.
Repeat this process twice more, or until you have used all the dough and butter mixture.
Bake until golden brown on top, 30 to 35 minutes, covering with foil if the top starts to brown too quickly.
For the glaze: Meanwhile, beat the cream cheese with the confectioners' sugar until smooth and light. Add the milk and vanilla and mix until fully incorporated. If the glaze seems too thick, add more milk. If the glaze seems too runny, add in a bit more confectioners' sugar. (You are looking for a gravy-like consistency, where the glaze will fall over the sides of the monkey bread but not spill off completely.)
Remove the monkey bread from the oven and cool for 10 minutes in the pan. Invert onto a serving plate.
Whisk the glaze briefly, then pour over the monkey bread. Garnish with more sprinkles.