Start by greasing a bundt pan thoroughly with softened butter, making sure every corner is coated well to prevent sticking.
In a bowl, combine warm milk, warm water, melted butter, sugar, and yeast. Let the mixture sit briefly so the yeast activates.
Add flour and salt to a mixing bowl, then pour in the yeast mixture. Knead until a smooth, slightly sticky dough forms. Adjust with small amounts of flour if needed.
Transfer the dough to a greased bowl, cover, and let it rise in a warm place until doubled in size.
Once risen, gently deflate the dough and move it to a lightly floured surface. Shape it into a rectangle and cut into small pieces, then roll each piece into a ball.
Place melted butter in one bowl and mix brown sugar with cinnamon in another. Dip each dough ball into butter, then coat in the sugar mixture.
Arrange the coated dough balls in the prepared pan, layering them evenly. Cover and let rise again until puffed.
Preheat the oven and bake until the top is golden brown and the bread is fully cooked through.
Allow the bread to cool briefly, then invert onto a serving plate while still warm.
Prepare the glaze by mixing powdered sugar, milk, and vanilla until smooth, then drizzle over the bread before serving.