Pour water into a large bowl and sprinkle in yeast. Let stand until yeast softens, about 5 minutes. Add sugar, eggs, 3 tablespoons oil and salt and stir to dissolve yeast. Gradually stir in enough flour to make a soft dough (you may have to use your hands to work in last additions). Work dough in bowl to make a smooth mass.
Lightly brush top of dough with additional oil. Cover bowl tightly with plastic wrap. Let stand in a warm place until doubled in volume, about 1 hour.
Brush two 9 or 10-inch round cake pans lightly with melted butter. Punch down dough and cut into 24 pieces. With floured hands, form each piece of dough into a ball. Arrange 12 balls of dough, smooth side up, in each pan. Cover loosely with plastic wrap and let stand in a warm place until almost doubled in volume, about 35 minutes.
Meanwhile, position a rack in the center of oven and preheat to 400 degrees F. Brush tops of rolls with remaining melted butter. Bake until golden brown, about 20 minutes.
Let rolls stand in pan for 5 minutes. Unmold and break the rolls apart. Serve rolls hot or warm.