Generously butter a 9-by-5-inch (23-by-13-cm) loaf pan, Pullman pan, or Bundt pan.
Dust the surface of the refrigerated dough with flour and cut off a 1 1/2-pound (680-g) piece. Divide the dough into about 32 equal pieces. Roll the dough into small balls. If the dough is sticking to your hands, coat your palms with a small amount of butter.
In a small saucepan set over low heat, melt 4 tablespoons butter. (Alternatively, you can microwave the butter in a small bowl to melt.) In a shallow bowl, stir together the granulated sugar and cinnamon.
Working with one ball at a time, drop the dough ball into the butter and then roll it in the cinnamon sugar. Place the balls in the prepared pan.
Let the dough rise at room temperature for about 1 hour.
While the dough is rising, preheat the oven to 350°F (180°C). Adjust the oven rack to the middle position.
In a small saucepan over low heat, melt 4 tablespoons butter. Add any remaining cinnamon sugar, the brown sugar, the salt, and the vanilla.
Pour the warm brown sugar mixture over the dough balls in the pan. Place the pan on a rimmed baking sheet lined with foil in case the caramel bubbles over the top. Bake until the surface of the bread is golden brown and seems caramelized and set, 30 to 40 minutes.
Let the bread cool for about 5 minutes in the pan. Place a platter or cutting board on the pan, turn it upside down, and then remove the pan. Serve warm.