In a large bowl, mix the starter, milk, honey, and butter until mostly smooth.
Add the flour and salt.
Stir until a shaggy dough forms.
Rest the dough for 20 to 30 minutes.
Knead for 3 to 5 minutes, until smoother.
Cover and let rise until puffy, about 4 to 8 hours.
Sprinkle in the baking soda and knead gently until fully worked in.
Chill the dough for 30 minutes if it feels very sticky.
Roll the dough to about 3/4-inch thickness on a cornmeal-dusted surface.
Cut rounds with a 3-inch cutter.
Place rounds on a cornmeal-dusted tray and rest 30 to 45 minutes.
Heat a skillet over low heat and lightly grease it.
Cook muffins for about 5 to 7 minutes per side.
If needed, finish them in a 300°F oven for 5 minutes.
Cool before splitting with a fork.