In a large bowl, stir together the starter and milk until well-combined. Add the flours and caraway seeds and stir until smooth. Cover the bowl with plastic wrap and a kitchen towel and let sit on the counter overnight, eight to twelve hours.
The dough should have increased in size overnight. Stir in the honey, salt and baking soda. The mixture will be sticky and loose and this is okay. Transfer the dough to a well-floured surface and sprinkle the top liberally with more flour. Take one portion of the dough, pull and fold over itself, keeping a ball shape. Repeat this several times, adding more flour as necessary. You may need to up to an additional 1/4-1/3 cup of flour. Note: A dough scraper would also be helpful in managing the dough by scraping from the bottom then folding the dough up over itself instead of using your hands.
Flatten the dough with your fingers to roughly 1/2 - 3/4 inch thick. Sprinkle a little more flour on top. Dust your round cutter with flour, too. I use one that is about 2 3/4 inches in diameter. Cut the dough into rounds and transfer the rounds on a baking tray generously dusted with corn meal. Lay the rounds on the baking tray. Shape the dough scraps into a ball and flatten again to collect more rounds. You should have 9-12 rounds, depending the size cutter you use. Dust the tops of the rounds with more corn meal then cover the tray with plastic wrap and leave to rest for 45 minutes to one hour.
Preheat your oven to 325ºF. Heat a cast iron skillet over medium heat and apply a light brushing of butter. Cooking in batches, cook each muffin for two minutes on each side or until lightly brown. Transfer the browned muffins on the same baking sheet (you don't have to wipe off the corn meal). Finish the English muffins in the oven until they are cooked through, 10-15 minutes. Cool on a wire rack for a few minutes and enjoy. They are also great toasted the next day.
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