In a small bowl, stir yeast into water and let mixture stand until bubbling, about 10 minutes. Meanwhile, warm milk and butter in a small saucepan over low heat until it bubbles. Remove from heat and stir in honey until dissolved. Let milk mixture cool to lukewarm.

In bowl of a standing mixer fitted with bread hook, combine 3 cups flour, salt, yeast mixture, and milk mixture. Mix at low speed until combined. Add remaining flour, 1 cup at a time, until a soft dough forms. Increase speed to medium and continue to knead dough until soft and smooth, 5–6 minutes.

Coat inside of a large bowl with olive oil and place dough in bowl, turning to coat all sides. Cover bowl with a damp cloth and allow to rise in a warm place until doubled in size, about 1 hour. Punch down dough and turn it out onto a floured surface. Roll it out to about ½-inch-thick. Cut out rounds with a biscuit cutter or drinking glass (a wide-mouth Mason jar is the perfect size).

Sprinkle a baking sheet with cornmeal and set the rounds on this to rise; dust tops with more cornmeal. Cover baking sheet with damp cloth and let muffins rise for 30 minutes.

Heat a lightly oiled griddle over low heat. Cook muffins on griddle until bottoms are golden brown, about 8–12 minutes on each side. (If the outsides are done before the insides, finish them off for 10 minutes in a 350° oven.) The English muffins can be stored in an airtight container for 3 days, or freeze them for up to 1 month. Serve them split and toasted.