1. 1. Activate the Yeast: In a large mixing bowl, combine the warm water, active dry yeast, and granulated sugar. Stir gently and let it sit for 5-10 minutes until the mixture becomes foamy. This foaminess indicates that your yeast is active and ready to work.

2. 2. Combine Wet Ingredients: Add the sourdough starter discard (or your flour and water mixture) and olive oil to the yeast mixture. Stir until well combined.

3. 3. Add Dry Ingredients: Gradually add the all-purpose flour and salt to the wet ingredients. Mix with a wooden spoon or your hands until a shaggy dough forms.

4. 4. Knead the Dough: Turn the dough out onto a lightly floured surface. Knead for 8-10 minutes until the dough is smooth and elastic. It should spring back when gently poked. If using a stand mixer, use the dough hook attachment and knead on medium speed for 6-8 minutes.

5. 5. First Rise (Proofing): Lightly grease a clean bowl with olive oil. Place the dough in the bowl, turning once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 60-90 minutes, or until doubled in size. The dough should look puffy and feel light.

6. 6. Shape the Rolls: Gently punch down the risen dough to release the air. Divide the dough into 6-8 equal pieces. On a lightly floured surface, shape each piece into an oblong sub roll shape, about 6-8 inches long. Place the shaped rolls on a baking sheet lined with parchment paper, leaving some space between them.

7. 7. Second Rise: Cover the baking sheet loosely with plastic wrap or a clean kitchen towel and let the rolls rise again for 20-30 minutes, or until noticeably puffy.

8. 8. Bake the Rolls: Preheat your oven to 375 F (190 C). If desired, brush the tops of the rolls with the beaten egg wash and sprinkle with sesame or poppy seeds. Bake for 15-20 minutes, or until golden brown and cooked through. The internal temperature should be around 200-210 F (93-99 C). Let them cool on a wire rack before slicing and serving.