It’s best to use a stand mixer fitted with a dough hook. You can also do this by hand or with an electric mixer, but it will take longer.
Combine 2 cups flour, sugar, dry yeast and salt in a large mixer bowl and whisk until blended.
Combine milk, water and butter in a microwave-safe bowl or measuring cup. Microwave on HIGH in 15 second increments until very warm but not hot to the touch, about a minute (120° to 130°F; butter won’t melt completely). Add to flour mixture with egg.
Beat 2 minutes at medium speed, scraping bowl occasionally. Add another 1 cup flour; beat 2 minutes at high speed, scraping bowl occasionally. Stir in just enough remaining flour so that the dough will form into a ball.
Knead on lightly floured surface until smooth and elastic and dough springs back when lightly pressed with 2 fingers, about 6 to 8 minutes. Cover with a towel; let rest for 10 minutes.
Make the coating: melt the butter and place in a small bowl. Mix granulated sugar and cinnamon in another small bowl.
Cut dough into 36 pieces (cut in half, cut each half in thirds and each third into thirds again, then each third in halves). Dip each piece into the melted butter and then roll in the cinnamon sugar mixture.
Spray pan with cooking spray. Place dough into pan. Combine remaining butter and sugar and drizzle over rolls. Cover with towel; let rise in warm place until doubled in size, about 45 minutes.
Make the topping: add remaining ¼ butter to the rest of the melted butter in the small bowl and heat until all melted. Add remaning cinnamon sugar mixture to the melted butter along with brown sugar and additional cinnamon. Stir to combine. Pour this mixture over the monkey bread pieces in the pan.
Allow to rise until about doubled in size; approximately 1 hour. It's helpful to place it in a warm place (i.e. on your stove top while the oven is preheating).
Preheat oven to 375°F.
9x13-inch baking dish: place dough pieces into single layer. After rising, bake for about 20 minutes or until golden and cooked through.
Fluted tube pan or Bundt pan: bake for about 40-50 minutes, or until golden and cooked through.
Two 9x5-inch bread pans: bake for about 20 minutes, or until golden and cooked through.
12 monkey bread muffins: place 3 pieces in each greased muffin cup. Bake for about 20 minutes, or until golden and cooked through.