Preheat oven to 350°F. Mix milk, gravy mix, and melted butter with a whisk in a large bowl. Reserve 3/4 cup of the gravy mixture; set aside.
Cut biscuits into quarters. Add biscuit pieces to gravy mixture in a large bowl; mix until all pieces are covered. Stir in 1 3/4 cups of the cheese and cooked Goetta until well blended. Place biscuit mixture into a greased bundt pan. Pour reserved gravy mixture over top.
Bake 35 minutes. Sprinkle with remaining 1/2 cup cheese. Bake 5 minutes longer or until cheese is melted. Cool in pan 5 to 10 minutes. To unmold, loosen sides of monkey bread from the pan with a knife. Place a plate on top of the pan then carefully flip the pan onto the plate. Remove the pan, place a second plate on top of the bread and flip again to leave the bread cheesy side up. Serve warm and share with friends and family.