In a medium mixing bowl, combine warm water, sourdough starter, white flour, whole wheat flour, sesame seeds, sesame oil and salt. Mix until a shaggy dough forms.
Cover the bowl and let the dough rest for one hour.
After resting, do a single round of stretch and folds around the dough to develop structure. Once smooth, cover the dough and let it rest until doubled in size (3-6 hours if in a warm spot, 6-12 hours if cooler).
Once the dough has doubled, generously sprinkle cornmeal on your work surface. Gently pour out the dough and spread it out with your hands into a large rectangle, about 6"x 12". Once it's large enough for 8 English muffin cut-outs, sprinkle more cornmeal on top, ensuring both sides of the dough are coated.
Using a bench scraper or similar object, cut out 8 squares/rectangles and transfer them gently to a cutting board. If the dough starts to stick, add a bit more cornmeal. Cover the muffins with a cotton towel while you preheat your pan.
Heat your non-stick or cast-iron pan on medium-low heat for 5 minutes.
Place as many muffins as will fit in the pan, ensuring they aren't touching. Cover with a lid and cook for 2-3 minutes, then flip and cook for another 2-3 minutes. They should bubble up and develop a golden brown crust. If they’re burning, lower the heat and let the pan cool before continuing.
Once cooked, place the muffins on a cooling rack or back onto the cutting board with the cotton towel. Let them cool, then slice and enjoy, filled with a generous amount of butter to fill those perfect air pockets!