Warm your milk, water, and melted butter together, then stir in the sugar and yeast so it can activate. Combine the flour and salt in your mixer bowl, then slowly pour in the wet mixture while the dough hook runs on low speed. Increase to medium speed and knead for about six to seven minutes until the dough turns smooth and elastic.
Transfer the dough to a greased bowl and cover it loosely with plastic wrap. Place it in a slightly warm oven, around 85°F, and let it rise until doubled in size, which usually takes about an hour. This first rise builds the soft, fluffy texture you want in the final bread.
While the dough rises, stir the brown sugar and cinnamon together in one bowl and melt the remaining butter in another. Keep both within reach near your workstation. This coating is what turns simple dough balls into that sticky, irresistible monkey bread everyone loves.
Pat the risen dough into an eight-inch square, then cut it into sixty-four small, even pieces. Roll each piece into a ball, dunk it in the melted butter, then roll it through the cinnamon-sugar mixture until fully coated.
Arrange the coated dough balls in your greased Bundt pan, staggering the second layer over the seams of the first for a more even bake. Cover loosely and let the pan rise again in a warm spot for about an hour, until the dough peeks above the rim.
Preheat your oven to 350°F and bake the monkey bread for thirty to thirty-five minutes, until the top turns a deep golden brown. Let it rest in the pan for five minutes before flipping it onto a serving plate so the caramel has time to set slightly.
Whisk the confectioners' sugar and milk together until smooth and pourable. Drizzle this glaze generously over the warm bread right before serving so it melts slightly into every crevice.