Warm the Greek yogurt in the microwave for 30 to 40 seconds and stir well to take the chill off. You want it warm, not hot, which helps the dough come together and keeps the fermentation moving.
In a large bowl or stand mixer, combine the warmed yogurt, water, egg, and honey. Add the active starter and stir to combine.
Add the flour, salt, and baking powder and mix until a shaggy dough comes together.
Once the dough is cohesive, add the softened butter and knead it in. Continue kneading 8 to 10 minutes by hand or 5 to 6 minutes with a dough hook on medium speed until the dough is smooth and supple. The dough will be soft and slightly tacky, which is correct, so resist adding extra flour. If your yogurt is very thick and the dough feels stiff like a bagel dough, work in extra water 1 tablespoon at a time until it softens.
Cover and rest the dough for 1 hour so the flour and yogurt fully hydrate. Then perform 2 to 3 sets of stretch and folds spaced about 15 minutes apart. This builds the strength that gives you an open, airy crumb.
Cover and ferment at room temperature for 8 to 12 hours, or overnight, until the dough has doubled and is puffy. In a warm kitchen, start checking earlier.
Dust a sheet pan generously with cornmeal. Divide the dough into 8 equal portions of about 116 grams each. If you want more muffins, make them a smaller amount.