- 11 tablespoons (1 3/8 sticks) unsalted butter, softened, plus more for the bowl, plus 5 tablespoons melted
- 1 envelope (1/4 ounce) active dry yeast
- 1 tablespoon sugar
- 2 tablespoon warm water (105°F to 110°F )
- 3/4 cup buttermilk
- 1 large egg, lightly beaten
- 2 3/4 cups plus 2 tablespoons all-purpose flour, plus more for the surface and pin
- 2 teaspoons salt
- 2 pounds sweet onions, such as Rio (1 1/2 pounds cut into 1/4-inch slices, 1/2 pound finely chopped)
- 1/8 teaspoon freshly grated nutmeg
Butter a 9-inch cake pan using 1 tablespoon softened butter. Butter a large bowl; set aside. Stir together the yeast, sugar, and warm water in a small bowl; let the mixture stand until foamy, about 5 minutes. Stir until dissolved. Stir in the buttermilk and egg.
Mix 2 3/4 cups flour and 1 1/2 teaspoons salt in the bowl of an electric mixer fitted with the dough hook. Make a well in the center. Pour in the buttermilk mixture; mix to combine. Add 6 tablespoons softened butter; mix on medium-high speed until a soft dough forms, about 10 minutes.
Scrape the dough onto a lightly floured work surface; sprinkle with the remaining 2 tablespoons flour. Knead the dough until smooth, about 5 minutes. Transfer to the buttered bowl. Cover the dough with a clean kitchen towel; let rise in a warm place until doubled in bulk, about 1 hour.
Melt the remaining 4 tablespoons softened butter in a large saucepan over medium-high heat. Add the onions; raise heat to high, and cook, stirring often, until soft, about 5 minutes. Reduce heat to medium; cook, stirring, until golden brown, about 30 minutes. Stir in the nutmeg. Season with 1/2 teaspoon salt. Let cool.
Punch down the dough, and turn out onto a lightly floured work surface. With a lightly floured rolling pin, roll the dough into a 17 x 10-inch rectangle, and brush with 3 tablespoons melted butter. Spread the onions evenly over the dough. Starting on 1 long side, roll the dough into a log. Press the seam to seal.
Cut into about 12 slices, about 1 1/4 inches thick each. Arrange the slices, cut sides up, in the buttered pan, and brush with remaining 2 tablespoons melted butter. Cover loosely with plastic wrap. Let rise in a warm place until doubled in bulk, about 50 minutes.
Preheat the oven to 375°F. Bake the rolls until golden brown, about 35 minutes. Immediately invert the rolls onto a wire rack. Serve warm.