In the bowl of a KitchenAid mixer, pour in the 1/2 cup warm water and 1 Tbsp sugar.
Sprinkle the yeast over the water and then let it rest for 2-3 minutes. Make sure the water is between 110-115 degrees Fahrenheit.
Add the 2 eggs, 3 Tbsp oil, 1 cup sourdough discard and 1 tsp salt and then mix gently until combined.
Add 3 cups of flour and then mix the dough using the dough hook until combined.
You may need to add more flour to make sure the dough is not sticky, just make sure to add it in 1/4 cup amounts until the right consistency is achieved.
Knead the sourdough roll dough using the dough hook on the KitchenAid mixer for 7 minutes or until the dough feels smooth.
Rest Dough
Grease a medium bowl and place the sourdough discard dough in and cover with a damp towel or plastic wrap, then allow the dough to rise for 1 hour.
Turn out the dough onto a slightly floured surface and then use a bench scraper to divide it into 12-15 dough balls of equal amount.
Roll the dough between your hands to make a smooth ball, then place the dough balls in a greased 9 X 13-inch baking pan.
Rise Dough Rolls
Cover the baking pan with plastic wrap and allow the dough to rise again until almost doubled which can take anywhere between 20 minutes to 1 hour.
If desired, in a small bowl, whisk one egg and then use a pastry brush to brush the tops of each roll.
Once baked, they have a glossy-browned look.
Finally, bake the rolls in an oven preheated to 375 degrees Fahrenheit for 20-25 minutes.