In the bowl of a stand mixer fitted with the dough hook, stir together warm water, yeast, and sugar. Let stand until creamy, about 5 minutes.
Lightly grease a 9×13 baking pan.
To the yeast mixture, add 2 tablespoon softened butter, 2 cups of flour, and salt (making sure that the salt is added on top of the flour and doesn't come in contact with the yeast until you begin mixing). Mix on low until the ingredients begin to come together.
Add remaining 2 cups of flour and mix again on low until flour is fully incorporated.
Increase the speed to medium and knead until the dough is smooth and elastic, about 5 minutes. (You will know it is ready when the dough starts to make a slapping sound as it hits the sides of the bowl.)
Remove the bowl from the mixer and cover it with a dish towel. Let the dough rise in a warm place until doubled in volume, about 20 minutes. (Note: I like to turn on the oven's light and let the dough rise inside the oven. The light produces just enough heat to help the dough rise quickly.)
Turn the dough out onto a lightly floured surface and form it into an even ball.
Using a serrated knife, cut the dough into quarters. Slice each quarter of dough into 6 even slices (you should have 24 even pieces of dough). With lightly floured hands, roll each piece of dough into a ball.
Place rolled dough in even rows in prepared pan.
Heat oven to 400°F / 200°C. Cover the rolls with a dish towel and put them near the warm oven to rise for 20 minutes.
Lightly brush the rolls with half of the melted butter (reserve the other half).
Bake until golden brown, 18 to 22 minutes.
Immediately after removing the rolls from the oven, brush them with the remaining melted butter and sprinkle with salt.
Flip the pan over to remove the rolls.