In a small bowl, combine the warm water and milk. Sprinkle the Fleischmann's RapidRise Yeast over the liquid and let it sit for about 5 minutes until frothy.
In a large mixing bowl, whisk together 3 cups of flour, granulated sugar, salt, and 1 tablespoon of ground cinnamon.
Add the melted butter and the activated yeast mixture to the dry ingredients. Beat in the egg until well combined. Gradually add more flour if too sticky.
Turn the dough onto a floured surface and knead for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with plastic wrap or a kitchen towel, and let it rise in a warm place for about 30-40 minutes until doubled in size.
In a separate bowl, mix together 1 cup granulated sugar, ½ cup brown sugar, and 1 teaspoon ground cinnamon for the coating.
Punch down the risen dough and tear off small pieces, rolling each into a ball. Dip in melted butter, then roll in the cinnamon sugar mixture.
Place the coated dough balls into the greased bundt pan, layering them as you go, and drizzle remaining melted butter over the top.
Cover the bundt pan with a kitchen towel and let it rise again for about 20-30 minutes until risen to the top of the pan.
Preheat your oven to 350°F (175°C) and bake for 30-35 minutes until golden brown and sounds hollow when tapped.
Let the Monkey Bread cool in the pan for about 10 minutes, then invert onto a serving plate. Serve warm, pulling apart pieces with your hands.