Ensure your sourdough starter is active and bubbly. If it has been in the refrigerator, take it out a day before and feed it with equal parts flour and water until it becomes vigorous.
In the electric stand mixer with the dough hook attached, combine the active sourdough starter, warm water, and warm milk until it is well combined. Wait 5 minutes.
Now add TWO CUPS of all-purpose flour, and mix until a sticky dough comes together. Cover and leave for 30 minutes. Mix the ingredients until they come together into a sticky dough.
Now add in the remaining 3 cups of all-purpose flour and honey. Knead the dough for about 5 minutes and a smooth elastic dough forms. Drizzle the olive oil on top and cover the top with plastic. Rest for 4-6 hours until it double in size.
Once the dough has risen, gently deflate it and turn it out onto a floured surface. Roll the dough to about 1/2 inch thickness. Using a round cutter or a glass, cut out individual muffins. Place them on a baking sheet dusted with cornmeal to prevent sticking.
Cover the muffins with a kitchen towel and let them rise for another 1-2 hours. They should puff up but not necessarily double in size.
Preheat a large skillet over medium-low heat. Sprinkle some cornmeal on the hot surface. Carefully transfer the muffins onto the skillet and cook for 6-8 minutes on each side or until they are golden brown and cooked through.
Once cooked, transfer the English muffins to a wire rack to cool. They can be split with a fork or a serrated knife.