Stir the flour, yeast and salt together. Add the lukewarm milk, ¼ cup sugar, egg and 3 tablespoons melted butter. Mix to a shaggy dough, then knead on a lightly floured surface for 8–10 minutes until smooth and elastic. It should feel soft and slightly tacky; add flour only a teaspoon at a time if it is unmanageably sticky.

Place in a lightly greased bowl, cover, and let rise in a warm draft-free spot for about 60–90 minutes, until doubled. Grease a 10–12-cup single-piece Bundt pan generously.

Combine the ½ cup granulated sugar and cinnamon in one bowl. Divide the dough into about 48 roughly equal pieces and roll into small balls. Dip each in the 6 tablespoons melted butter, then roll in cinnamon sugar. Arrange loosely in the prepared pan. Mix any remaining butter with the brown sugar and vanilla, then distribute over the dough.

Cover and let rise for 35–45 minutes, until the pieces are visibly puffy. Toward the end of the rise, heat the oven to 350°F (175°C), with a rack in the lower-middle position.

Set the pan on a rimmed baking sheet and bake for 30–40 minutes. The top should be deeply golden and a thermometer inserted into the bread, not a sugar pocket, should reach about 190–195°F. Loosely tent with foil if it browns before the center is baked.

Rest in the pan for 10 minutes. Wearing oven mitts, place a large rimmed platter over the pan and invert carefully. Lift off the pan and cool another 10 minutes before serving warm. The melted sugar is very hot.