Combine warm milk, yeast, and 1 teaspoon sugar in a large bowl; let stand 5-10 minutes until foamy.
Add melted butter, remaining sugar, egg, vanilla extract, and salt; stir well to combine.
Gradually add flour, 1 cup at a time, mixing until a shaggy dough forms.
Turn dough onto floured surface and knead 5-7 minutes until smooth and elastic, or use a stand mixer with a dough hook.
Place dough in a lightly oiled bowl, cover with plastic wrap or kitchen towel, and let rise in a warm place for 1 to 1.5 hours until doubled.
Mix granulated sugar and cinnamon in a shallow bowl; melt remaining butter in another bowl.
Punch down the dough and roll out to 1/2-inch thickness on floured surface.
Cut dough into about 1-inch pieces using a pizza cutter or knife.
Dip each piece into melted butter, then toss in cinnamon-sugar mixture.
Place coated dough pieces into a greased bundt pan, evenly distributing the fresh blueberries among the dough.
Cover bundt pan with plastic wrap or towel and let rise in a warm place for 30 minutes.
Preheat oven to 350°F (175°C).
Bake monkey bread for 40-45 minutes until golden and cooked through; loosely cover with foil if browning too quickly.
Cool bread in pan for 10 minutes, then invert onto serving plate.
Optional: Whisk powdered sugar, milk or cream, and vanilla until smooth; drizzle over warm monkey bread before serving.