Add the sourdough starter, sugar and water to a mixing bowl and stir until dissolved.
Now pour the oil in, then add the flour and salt on top of that.
Bring the ingredients together into a dry, shaggy dough. Cover the bowl and allow to sit for around an hour.
Now, tip the dough out onto a clean surface and knead it until the dough is soft and elastic. You can easily knead this dough by hand, but if you prefer, you can use a stand mixer with a dough hook on low speed or a Thermomix on the dough knead setting.I find it takes around 10 minutes to knead the dough sufficiently by hand. Once the dough is smooth and supple, place it back into a covered bowl and place it somewhere warm to bulk ferment. For these rolls, you don't want the dough to double, you want it to rise around 50%.
When the dough is ready, tip it out onto a clean surface and divide the dough into four equal pieces. I weigh my dough and usually make them around 200 to 225g each (depending on my final dough weight).
Pull each piece of dough into a rough rectangle, with the long edge in front of you. Then roll the dough up into a log and gently pinch the ends to seal them off. Repeat this for each piece of dough.
Use a dough scraper to transfer the sourdough sandwich rolls to a baking tray lined with parchment paper. Use your finger tips to flatten the dough out a little so that there is more surface area. Cover with a damp kitchen towel and allow them to proof. They need to get really soft and puffy before you bake them. When you're ready to bake the sandwich rolls, preheat your oven to 200C. Lightly egg wash the rolls and then slash them with a lame or sharp knife.
Bake them in the oven until just golden. This will take around 25 to 30 minutes depending on your oven. You don't want to over bake them or they will be too crispy on the outside.
To keep the outside soft, brush the sourdough sandwich rolls with butter as soon as they come out of the oven.
Allow baked sourdough sandwich rolls to cool on a wire rack.