In a large measuring cup or bowl, mix together the milk, water, melted butter, sugar, and yeast.
In a stand mixer fitted with the dough hook, add the flour and salt. With the mixer on low speed, add the milk mixture. Increase to medium speed and knead until the dough is smooth, 5 to 7 minutes. Add additional flour a couple tablespoons at a time only if the dough is sticking to the bottom of the sides of the bowl. After kneading, the dough should be soft, supple and slightly sticky without leaving a lot of dough residue on your fingers.
Place the dough in a lightly greased bowl, cover, and let the dough rise until doubled, 1 to 2 hours.
Spread the softened butter evenly in a 12-cup bundt pan, using a pastry brush or piece of wax or parchment paper to ensure all the nooks and crannies of the pan are well-buttered. Set aside.
Lightly punch down the dough. On a very lightly floured or greased countertop, press the dough into a thick rectangle or square, about 8 or 9 inches across. Use a bench scraper or pizza cutter to cut the dough into 64 small pieces.
Roll each piece into a round ball shape. It doesn't have to be perfect.
Combine the brown sugar and cinnamon in a bowl or shallow dish.
Dip the dough pieces in melted butter and then roll evenly in the sugar mixture. Place the dough pieces in the prepared Bundt pan, offsetting the dough balls so they aren't stacked exactly on top of each other.
Cover the Bundt pan and let the bread rise until noticeably puffy and nearly doubled, 1 to 2 hours.
Preheat the oven to 350 degrees F. Uncover the bundt pan and bake until the bread is golden brown and the bread is baked through, 30 to 35 minutes. An instant-read thermometer inserted into the bread should read 190 to 200 degrees F.
Cool the monkey bread in the pan for no longer than 5 minutes (any longer and the bread will be too sticky and hard to remove!). Turn the bread onto a platter.
In a small bowl, whisk the confectioners' sugar and milk together until smooth. Drizzle the glaze over the top and sides of the warm monkey bread. Serve warm.
Notes
Monkey Bread without a Mixer: mix the flour and salt in a large bowl. Make a well in the flour, then add the milk mixture to the well. Using a wooden spoon, stir until the dough becomes shaggy and is difficult to stir. Turn it out onto a lightly floured work surface and begin to knead, incorporating the shaggy scraps back into the dough. Knead until the dough is smooth and satiny, about 10 minutes. Shape into a taut ball and proceed as directed.Make-Ahead Instructions: after assembling the monkey bread in the pan, cover the pan with plastic wrap and immediately place the pan in the refrigerator, up to 12-18 hours. A couple hours before you want to bake it, remove the pan from the refrigerator and let the monkey bread come to room temperature and rise until puffy and risen 1-2 inches below the top of the pan (this exact measurement will depend on the dimensions of the Bundt pan you are using). Bake as directed in step #7 and proceed with the recipe.