Heat milk in the microwave on high for 45-60 seconds until warm but not hot.
Stir in sugar and yeast with a whisk. Let sit for 5-10 minutes until foamy.
Pour yeast mixture into the bowl of a stand mixer (or a large bowl if kneading by hand), and whisk in softened butter, eggs and salt. The butter may be slightly lumpy but that is fine.
Place the bowl in the stand mixer and attach the dough hook.
Turn the mixer to low speed and add the flour one cup at a time, waiting until it is mostly incorporated before adding more. Add enough flour so that a soft but not sticky dough forms.
Drizzle a clean bowl with oil and place dough in the bowl. Turn to coat the dough in oil and cover with plastic wrap or a clean kitchen towel and set in a warm, draft-free place to rise for 1-1.5 hours until doubled in size.
In a medium saucepan, combine butter, brown sugar and cream.
Bring to a boil over medium-high heat, whisking constantly, and cook 2-3 minutes. Set aside.
Cinnamon Sugar Coating
Place melted butter in a small bowl.
In another small bowl, combine sugar and cinnamon. Set aside.
Grease a 12 cup bundt pan well and pour the caramel sauce in the bottom.
Once dough has risen, tear into small pieces and roll into balls -- they don't have to be pretty!
Dip balls in melted butter, then coat in cinnamon sugar before placing in the prepared bundt pan. Repeat until all the dough has been used.
Set in a warm, draft-free place to rise for 30-60 minutes until puffed slightly.
Bake at 350 degrees for 35-40 minutes, until top is light golden brown.
Let cool in pan for 10 minutes before gently loosening with a small spatula or knife, then inverting onto a large round plate.
In a small bowl, whisk together powdered sugar and just enough milk to make a thick glaze. If necessary, add additional powdered sugar to thicken to desired consistency. Pour over monkey bread while warm and serve.