3 medium yellow onions, finely chopped
1/4 cup plus 1 teaspoon granulated sugar
kosher salt
2 (0.25 oz) packages active dry yeast
2 large eggs
6 Tablespoons butter, melted, plus more for shaping the dough
6 cups all-purpose flour, spooned and leveled, plus more for shaping the dough
Heat 2 Tablespoons of the oil in a large skillet over medium high heat. Add the onions, 1 teaspoon of the sugar, and 1/2 teaspoon salt and cook, stirring occasionally, until golden brown, 15 to 18 minutes. Place 2 cups warm tap water (105 degrees F to 115 degrees F) in a large bowl; sprinkle with the yeast and let stand until foamy, 4 to 5 minutes. Whisk in the eggs, 4 Tablespoons of the butter, the remaining 1/4 cup sugar and a 1/2 teaspoon of salt. Add the flour and three-quarters of the onions and mix until a sticky dough forms. Brush the top of the dough with the remaining tablespoon of oil . Cover the bowl with plastic wrap and let rise in a warm place until doubled in bulk, about 1 hour. Butter a 13 x 9 baking pan. Punch the dough down. With well-floured hands, form the dough into 16 balls and place in the prepared pan, spacing evenly. Sprinkle with the remaining quarter of the onions. Cover the pan loosely with plastic wrap and let rise in a warm place until doubled in bulk, 30 to 40 minutes. Preheat oven to 400 degrees F. Remove the plastic wrap and brush the dough with the remaining 2 Tablespoons of butter. Bake until the rolls are golden, 18 to 22 minutes (tent with foil if tops brown to quickly-I did). Cool in the pan for five minutes before serving.