Activate the Yeast: Pour the warmed milk into a large mixing bowl or the bowl of a stand mixer. Sprinkle the yeast and granulated sugar over the milk. Whisk gently to combine. Let this mixture sit for about 5 minutes until it becomes frothy, indicating the yeast is active and ready.
Combine Wet Ingredients and Start Dough: Add the eggs, melted butter, and salt to the yeast mixture. Stir briefly to incorporate. Begin mixing in 1 cup of flour using a dough hook or sturdy spoon until the ingredients start coming together.
Add Remaining Flour and Knead Dough: Gradually add the rest of the flour while mixing on medium speed. Continue kneading the dough—either in the mixer for about 5 to 7 minutes or by hand on a lightly floured surface. The dough should feel soft, slightly tacky, but not sticky. Perform a windowpane test by stretching a small piece of dough to check for gluten development. If the dough tears easily, knead a little longer.
First Proof: Lightly oil a large bowl and place your dough inside, turning once to coat. Cover the bowl with a clean towel or plastic wrap. Let the dough rise in a warm spot for 1.5 to 2 hours, or until it has roughly doubled in size.
Prepare Bundt Pan and Coating Mixture: Grease a 10-12 cup bundt pan thoroughly with butter or nonstick spray. In a small bowl, melt half of the butter (about ½ cup). In another bowl, combine the granulated sugar and cinnamon.
Shape Dough Balls: Once risen, punch down the dough gently to release air. Pinch off small pieces and roll them into approximately 1¼-inch diameter balls. Dip each ball into the melted butter, then roll it generously in the cinnamon-sugar mixture. Arrange the coated balls evenly in the bundt pan.
Let Dough Rest: Cover the filled bundt pan loosely with plastic wrap or a kitchen towel. Allow the dough balls to rest for 15-20 minutes to rise slightly.
Add Brown Sugar Glaze: Melt the remaining butter (¼ cup) and stir in the brown sugar and vanilla extract until smooth. Pour this mixture evenly over the dough balls in the bundt pan.
Bake Monkey Bread: Position the oven rack near the lower third and preheat your oven to 350°F (177°C). Bake the monkey bread for 35 to 45 minutes until it turns a rich golden brown. If the top darkens too quickly, tent loosely with foil.
Cool and Ice: Let the bread cool in the pan for about 5-10 minutes. Carefully invert it onto a serving platter. Mix the powdered sugar, milk, and vanilla extract until smooth and drizzle over the warm monkey bread. Serve warm, letting guests pull apart the gooey pieces.