Pour warm water into a large bowl; sprinkle with yeast, and let stand until foamy, about 5 minutes.
Add sugar, butter, eggs, and salt; whisk to combine. Add flour; mix until incorporated and a sticky dough forms. Brush top of dough with butter; cover bowl with plastic wrap, and set aside in a warm place until dough has doubled in bulk, about 1 hour.
Turn dough out onto a well-floured work surface. With floured hands, roll dough into a thick log. Cut into 18 equal pieces (halve log, cut each half in thirds, then cut each piece into thirds again).
Brush a 9-by-13-inch baking pan (I used a 9 x 9 pan) with butter. One at a time, flatten each piece of dough, then fold edges toward the center, pressing to secure, until a smooth ball forms. Place dough balls in prepared baking pan, smooth side up (you should have 3 rows of 6 *4 rolls of 4 in a 9x9 pan). Cover loosely with plastic wrap, and let rise in a warm place until doubled in bulk, 30 to 40 minutes. (Alternatively, refrigerate, at least 4 hours and up to 1 day.)
Preheat oven to 400 degrees. Remove plastic wrap; brush rolls with butter (I used an egg wash).
Bake until golden and rolls sound hollow when tapped on bottom, 35 to 40 minutes (tent with aluminum foil if browning too quickly). Pull rolls apart, and serve warm.