In a mixing bowl of a stand-up mixer, pour water, yeast, and sugar. Wait 5 minutes for the yeast to bloom.
Now start to mix the dough by using a paddle attachment (or use the dough hook the whole time) and adding in eggs, oil, and sourdough discard.
Mix well for 30 seconds.
Now change to a dough hook if you weren’t already using and add 3 ¼ cups of flour and salt, gradually. Mix for 4 minutes.
The dough may be sticky but when pushing in it, it won’t stick to your finger. If your dough is too sticky, you can add a ¼ cup of extra flour at this time. You should not have any flour dry in the bowl.
Transfer to a large, oiled bowl and cover with plastic wrap.
Put it in a warm place to allow for 60 minutes of rise time or until it doubles in size. This is called bulk fermentation when the dough is in its first stage of fermenting in a large, single mass.
Once it doubles in size, transfer to a lightly flour surface and divide the dough into 12 equal parts.
On the counter or a work surface, roll each ball. I make a dome with my hand and roll the ball between my hand and the counter. The round balls are then transferred to a buttered 9×13 baking dish to proof.
Next, cover with plastic wrap and let it rise for another 30-45 minutes in a warm place. Until it doubles in size. This is called proofing when the dough is in its final stage of rising.
Start your oven at 375-degree F.
Bake the rolls in preheated oven for 20 minutes. You can egg wash the buns if you like or butter them straight out of the oven.
As soon as they come out, brush with the melted butter on the buns.