Preheat the oven to 450 degrees F and place a 10-inch cast-iron pan in the oven to preheat.
Whisk the flour, baking powder, baking soda and salt in a large bowl to blend.
Using a pastry cutter, cut the cheddar cheese, half of the goat cheese and 4 tablespoons of cold butter into the flour mixture until the butter resembles small pea-size pieces.
Form a well in the center of the flour mixture and pour the buttermilk into the well.
Stir just until the mixture is moistened but still lumpy.
Fold in the remaining goat cheese.
Remove the cast-iron pan from the oven and melt 1 tablespoon of butter in the pan.
Drop 6 mounds of dough into the hot pan, spacing evenly apart.
Brush the tops of the biscuits generously with some of the melted butter.
Bake 10 minutes. Brush with some of the remaining butter and continue to bake until golden brown on the top and the bottom, about 10 minutes longer.
Remove the pan from the oven then brush the biscuits with the remaining melted butter and sprinkle with the Parmesan cheese. Cool slightly.
Serve warm and enjoy.
