Mix together the flours, sea salt, sugar and yeast in a large bowl.
Heat the buttermilk and 2 tablespoons of butter in a saucepan over low heat just to warm the buttermilk and melt the butter. It shouldn't go above 110° F or it may kill the yeast.
Once the butter has melted, stir the buttermilk mixture into the dry ingredients, and keep stirring until everything is well incorporated and the batter starts to look smooth and shiny, about five minutes. It will be a very sticky dough, so just scrape it all towards the middle of the bowl in a rough ball shape.
Cover with a cloth and set in a warm place to rise until almost doubled in size, approximately 30 mins to an hour, depending on how warm your kitchen is.
Place a cast-iron skillet over low heat on the stovetop. (It really does need to be quite low, I had mine on what I thought was low at first, but it browned the first muffins a bit too quickly, so they didn't rise as much as the following muffins did after I turned the heat down a bit to "1" on my burner dial.)
Turn out onto a generously floured counter, punch down, and divide into 12 pieces.
Knead and roll each piece between your hands to form a ball, and place this ball on a piece of parchment paper to rise. Slightly press down each ball so they are more of a disk shape than a ball. Continue with the rest of the dough. Cover with a sheet of parchment and allow to rise until increased by half (about 15 to 20 minutes).
Preheat oven to 400°F.
Sprinkle a bit of cornmeal over each muffin and place as many will fit on your pan with some room to spare, cornmeal side down (I cooked three at a time). Sprinkle a bit more cornmeal on the upper side of the muffin, and let cook for 8 to 10 minutes, until the underside is a light golden brown. Then flip over and cook the other side for an additional 8 to 10 minutes. For some of my muffins, I let them cook free-form, and then for others I used the English muffin rings. Both ways are fine, the muffin ring muffins just look a bit neater and are more uniform in size.
Once the muffins have finished cooking on the stovetop, transfer them to a baking sheet and continue to bake them in the oven on the middle rack for another six minutes. This just ensures that the insides are cooked through.
Transfer to a cooling rack and allow to cool before splitting with a fork to toast.