Mix together Sourdough Starter and buttermilk.
Combine flour, 4 tablespoons of the cornmeal, soda, and salt; add to buttermilk mixture.
Stir to combine well.
Turn out onto lightly floured surface and knead till smooth and elastic, adding more flour if necessary.
Roll dough to 3/8-inch thickness.
Let rest a few minutes.
Using a 3-inch cutter, cut dough into muffins.
Sprinkle sheet of waxed paper with 7 tablespoon of the cornmeal; place muffins atop, and sprinkle with the remaining cornmeal.
Cover and let rise till very light (about 45 minutes).
Bake on medium-hot, lightly greased griddle about 30 minutes, turning often.
Split; toast and serve with butter.