Combine the warm water, sugar and yeast together in a glass measuring cup and let yeast ferment until foamy, about 5 to 10 minutes. Whisk flour and salt together in a large bowl. Make a well in the flour, add 1 of the eggs and 1 yolk into the well and slightly beat Add the yeast mixture and stir with a wooden spoon until a rough dough forms. Turn out onto a lightly floured surface and knead, adding more flour as needed, until dough is smooth and elastic.
Place in a bowl, cover with a kitchen towel and let dough rest for 10 or 20 minutes. Remove dough from the bowl, divide the dough in half and roll each piece into a long 1 1/2-inch wide snake shape. Cut into 20 pieces and shape each into a ball.
Coat a 9-inch glass pie dish the melted butter, then toss the dough balls in the butter until coated. Cover with a kitchen towel and sit in a warm place, until dough doubles in size, about 1 hour.
Preheat oven to 400 degrees F.
Brush the tops of the rolls with the remaining egg and sprinkle with the coarse salt. Bake until golden brown, about 25 to 30 minutes. Let cool about 30 minutes but serve warm.