Pour the warm water into the bowl of a standing electric mixer, add the yeast and granulated sugar, and let the yeast proof until bubbly on the surface, about 10 minutes.
Meanwhile, in a medium saucepan, heat the 2 cups of milk until very warm (120 to 130 degrees F).
In another pan, melt the butter. Set aside 1/4 cup for brushing the pans.
When the yeast is bubbly, fit the electric mixer with a dough hook or paddle. Add all of the flour, the brown sugar, warm milk, eggs, and the 1 1/4 cups melted butter and beat on low speed for 10 minutes.
Oil a large bowl and place the dough in it, turning it in the bowl to coat on all sides. Cover and let rise in a warm, draft-free place until doubled in volume, about 1 1/2 hours.
Brush two 8-inch springform pans, 2 inches deep, with the reserved 1/4 cup of melted butter.
Make the filling: In a bowl, stir together the brown sugar, currants, and cinnamon.
Once the dough has doubled, punch it down with your hands. Divide the dough into 2 equal portions. On a clean, dry, lightly floured surface, roll out each piece of dough into a rectangle 8 x 12 inches. Sprinkle half the filling over each piece of dough, leaving a 1-inch border on all sides. Starting with the long side of the dough closest to you, roll each piece of dough into a cylinder, pinching the seam closed. Cut each roll into 6 equal slices and place the slices, cut side up, with the sides touching, in the prepared springform pans. Brush the surface of the buns with the remaining 1/4 cup of milk. Let the buns rise in the pans until almost doubled in size, about 30 minutes.
In the meantime, preheat the oven to 350 degrees F.
Bake the buns for about 45 minutes, until golden and a toothpick inserted into the center of one of the buns comes out clean. Cool in the pans 10 minutes. Serve warm. To store, wrap the buns well in plastic, then store in the refrigerator for up to 3 days. To reheat, remove the plastic wrap; then wrap the buns in aluminum foil. Reheat in a preheated 350 degree F oven for about 10 minutes, or until heated through.
Recipe courtesy MANGIA (HarperCollins, 2001) by Ricardo Diaz and Nancy Jessup