Whisk 1/4 cup flour, yeast, and 1/2 cup water together in a large bowl until foamy, about 10 minutes. Add oil, egg white, salt, remaining 1 ¾ cups flour, and remaining 1/4 cup water. Mix together until well combined; dough will be very wet and sticky. Cover, place in a warm spot, and let rise until double in size, about 2 hours.

Turn dough onto a well-floured surface. Work in just enough flour until dough is easy to work with, about 1 minute. Cut dough into 6 equal portions. Form each into a seamless dough ball, adding a pinch of flour to keep them from sticking to the work surface. Flatten to make thick disks. Transfer disks onto a lined baking sheet sprinkled generously with cornmeal. Let rise until double in size, about 1 to 1 ½ hours.

Add clarified butter to a large skillet over medium heat. Carefully transfer muffin disks to the skillet, cooking in batches to avoid overcrowding. Brown on both sides, turning halfway through cooking time, 10 to 12 minutes total. Continue turning to get muffins evenly brown and cooked through, 7 or 8 minutes more per side. Transfer to a rack to cool completely (this is key as you can't split muffins unless they're cool).