In the bowl of a stand mixer fitted with the paddle attachment, combine warm milk, sugar, and yeast. Let stand until mixture is foamy, about 10 minutes.

With mixer running on low speed, add 1 cup (125 g) flour, beating just until combined. Add melted butter and additional ½ cup (63 g) flour, beating until combined. Beat in eggs. Gradually add salt and remaining 1¾ cups (218 g) flour, beating until a soft dough forms. (Dough will be sticky.)

Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Loosely cover and let rise in a warm, draft-free place (75°F) until doubled in size, about 1 hour.

In one small bowl, combine the brown sugar and cinnamon. Stir to combine. In a second bowl, melt the butter.

Spray a 10-inch bundt pan with cooking spray.

Punch dough down very gently to release the gasses. Remove small amounts of dough to form into about 1-inch balls. Dip each ball of dough into melted butter first, then roll into the brown sugar-cinnamon mixture. Place each ball of dough into the prepared pan, arranging them as you go. You will get about 30 balls of dough. Cover the pan with a towel and allow to rise for another 45 minutes in a warm draft-free place.

Pre-heat the oven to 350°F. Combine the rest of the brown sugar/cinnamon mixture and butter. Pour the mixture over the monkey bread before baking. Bake in your pre-heated oven on the middle rack for 30-35 minutes. The internal temperature should read 190°F. Allow to cool in the pan for 5 minutes, before inverting onto a plate.

In a bowl, whisk together the powdered sugar, milk, and vanilla. Drizzle over the monkey bread and serve while warm.