For the Dough: Adjust oven rack to medium-low position and heat oven to 200 degrees. When oven reaches 200 degrees, turn it off. Butter Bundt pan with 2 tablespoons softened butter. Set aside.
In large measuring cup, mix together milk, water, melted butter, sugar, and yeast. Mix flour and salt in standing mixer fitted with dough hook, (see below for making Monkey Bread without a mixer). Turn machine to low and slowly add milk mixture. After dough comes together, increase speed to medium and mix until dough is shiny and smooth, 6 to 7 minutes. Turn dough onto lightly floured counter and knead briefly to form smooth, round ball. Coat large bowl with nonstick cooking spray. Place dough in bowl and coat surface of dough with cooking spray. Cover bowl with plastic wrap and place in warm oven until dough doubles in size, 50 to 60 minutes.
For the Sugar Coating: While dough is rising, mix brown sugar and cinnamon together in bowl. Place melted butter in second bowl. Set aside.
To Form the Bread: Gently remove dough from bowl, and pat into rough 8-inch square. Using bench scraper or knife, cut dough into 64 pieces.
Roll each dough piece into a ball. Working one at a time, dip balls in melted butter, allowing excess butter to drip back into bowl. Roll in brown sugar mixture, then layer balls in Bundt pan, staggering seams where dough balls meet as you build layers.
Cover Bundt pan tightly with plastic wrap and place in turned-off oven until dough balls are puffy and have risen 1 to 2 inches from top of pan, 50 to 70 minutes.
Remove pan from oven and heat oven to 350 degrees. Unwrap pan and bake until top is deep brown and caramel begins to bubble around edges, 30 to 35 minutes. Cool in pan for 5 minutes, then turn out on platter and allow to cool slightly, about 10 minutes.
For the glaze: While bread cools, whisk confectioners' sugar and milk in small bowl until lumps are gone. Using whisk, drizzle glaze over warm monkey bread, letting it run over top and sides of bread. Serve warm.
Monkey Bread Without a Mixer: In step 2, mix flour and salt in large bowl. Make well in flour, then add milk mixture to well. Using wooden spoon, stir until dough becomes shaggy and is difficult to stir. Turn out onto lightly floured work surface and begin to knead, incorporating shaggy scraps back into dough. Knead until dough is smooth and satiny, about 10 minutes. Shape into taut ball and proceed as directed.