Adapted from Cook's Illustrated
4 tablespoons unsalted butter , divided, 2 tablespoons softened and 2 tablespoons melted
1 cup milk , warm (about 110 degrees)
1/3 cup water , warm (about 110 degrees)
1/4 cup granulated sugar
1 package rapid-rise yeast (or instant)
3 1/4 cups all-purpose flour , plus extra for work surface
2 teaspoons table salt
Brown Sugar Coating
1 cup packed light brown sugar
2 teaspoons ground cinnamon
8 tablespoons unsalted butter (1 stick), melted
Glaze (I used more sugar, milk, melted butter and vanilla)
1 cup confectioners' sugar
2 tablespoons milk
Adjust oven rack to the bottom 1/3 of the oven and heat to 200º. When oven reaches 200º, turn it off. Grease Bundt pan with the 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. Turn machine to low and add milk mixture in slow stream. When dough comes together, increase speed to medium and mix 6 to 7 minutes. Remove from bowl, and knead briefly on lightly floured surface. Place in large bowl coated with cooking spray. Cover bowl with greased plastic wrap and place in warm oven until dough doubles, about an hour.
While dough is rising, combine brown sugar and cinnamon together in bowl. Put melted butter in second bowl.
Remove dough from bowl, and pat into an 8 inch by 8 inch square. Cut dough into 64 pieces.
Roll each dough piece into ball. Coat balls in melted butter, one at a time. Roll in brown sugar mixture, then place the balls in greased Bundt pan. When reaching second layer, place rolls over seams for a better presentation.
Cover pan tightly with plastic wrap and place in turned-off oven until dough has risen an inch or so below top of pan, about an hour.
Remove pan from oven and heat oven to 350 degrees. Bake until top is deep brown, about 30 to 35 minutes. Cool for 5 minutes, then turn out onto serving plate and allow to cool about 10 minutes before icing.
While bread cools, whisk icing ingredients until smooth. Drizzle glaze over warm monkey bread. Serve warm.