To make sweet dough:
Whisk 1 cup flour with 1/4 cup granulated sugar, yeast and salt in a large bowl. Whisk in milk, 1/3 cup hot water, 2 tbsp butter and egg. Using a wooden spoon, stir in 1 3/4 cups flour and continue stirring until dough starts to come together. Knead dough in bowl until smooth and not sticky, adding remaining flour as needed, 3 to 4 min. Cover loosely with a damp kitchen towel and let rest until dough is doubled in size, about 1 hour.
To make Monkey Bread:
Preheat oven to 350F. Spray a 10-in. Bundt pan lightly with oil.
Pour butter in a shallow dish. Stir brown sugar with cinnamon in a medium bowl. Shape Sweet Dough into 1-in. balls. Dip each ball in butter, then coat in sugar mixture. Stack in Bundt pan, staggering each layer like bricks. Pat down. Sprinkle any remaining butter and sugar over dough.
Bake in centre of oven until deep golden brown, about 25 min. Transfer to a rack. Let stand 5 min, then flip onto a plate.
Sift icing sugar into a medium bowl. Stir in milk, 1 tbsp at a time, until smooth. Drizzle glaze over warm Monkey Bread. Serve immediately.