How to Make It
Combine warm water, yeast, and 1 teaspoon of the sugar in a 1-cup liquid measuring cup; let stand until foamy, about 5 minutes.
Stir together eggs, buttermilk, kosher salt, 1⁄2 cup of the melted butter, and remaining 6 tablespoons sugar in a medium bowl. Add yeast mixture and 3 1⁄2 cups of the flour; stir until a dough forms. Sprinkle a work surface with 1⁄4 cup of the flour; turn dough out onto floured surface, and knead until smooth and slightly elastic, about 4 minutes, adding up to an additional 1⁄4 cup flour, if needed. Place dough in a lightly greased bowl; turn to grease top. Cover with plastic wrap, and chill 8 to 24 hours.
Coat 2 (12-cup) muffin pans with cooking spray. Punch chilled dough down, and turn out onto a lightly floured surface. Divide dough in half. Roll 1 dough half into a 16- x 12-inch rectangle (about 1⁄4 inch thick). Brush top with 2 tablespoons of the softened butter. Starting from a 12-inch side, cut dough into 6 (2-inch-wide) strips. Cut dough strips crosswise into quarters. (You will have 24 [4- x 2-inch] dough pieces.)
Stack 3 dough pieces together, buttered side up. Top with a fourth piece, buttered side down. Repeat with remaining 20 dough pieces, making 6 stacks. Cut each stack in half crosswise, making a total of 12 stacks of 2-inch squares. Place 1 stack on its side, layers facing up, in each muffin cup. Cover loosely with plastic wrap. Repeat process with remaining dough half, 2 tablespoons softened butter, and muffin pan. Let rolls rise in a warm (80°F to 85°F) place, free from drafts, until doubled in size, about 1 hour.
Preheat oven to 375°F. Bake rolls until golden brown, 12 to 15 minutes. Brush rolls with remaining 2 tablespoons melted butter, and sprinkle with desired amount of sea salt.