Heat the water and add the yeast on top. Let it sit about 5-10 minutes until if becomes foamy.
Whisk the sugar, eggs, butter and salt well. Add the flour and stir until you have a rough, sticky dough.
Brush the top of the dough with some melted butter, cover the bowl with plastic wrap and place the bowl in a warm area to rise for about an hour. Dough should double in size.
Turn the dough out on to a floured surface. Flour your hands and shape the dough into a log shape.
Cut the dough log into 18 equal pieces. Spray a 9 X 13 pan with cooking spray.
For each piece of dough, flatten it a bit and turn the corners underneath into the center. Place in the pan smooth side up in 3 rows of 6.
(If you are making ahead you can refrigerate the rolls up to a day at this point.)
Cover the pan with plastic wrap and let dough rise another 30-40 minutes. (If you are taking the rolls out of the refrigerator this will be more like 60 minutes.)
Preheat oven to 400 degrees.
Remove plastic wrap. Brush the top of the dough with remaining 1 tablespoon melted butter, spread caramelized onions evenly over top of rolls if using, and sprinkle dry onion soup mix evenly over the top of the rolls.
Bake at 400 degrees for about 35-40 minutes. Lay a sheet of foil over the top of the rolls after about 15 minutes. (The butter topping and onions have a tendency to burn). The rolls should sound a bit hollow when you tap them when they are done.