In a food processor, blend together the self-rising flour and 4 tablespoons of the butter until it resembles coarse cornmeal. Add another 4 tablespoons of butter and quickly pulse about 10 times until the butter pieces are about the size of large peas.
Add 3/4 cup of the yogurt and pulse 3 times to combine. Add another 3/4 cup of yogurt and pulse just until the dough starts to come together, 5 or 6 more times, adding the remaining 1/4 cup as needed.
Turn the rough dough out onto the counter and use a dough scraper to fold the dough over itself until a uniform dough forms, maybe 6 times.
Dust the counter with all-purpose flour and place the dough on top of the flour. Dust the top of the dough with more flour, then use the dough scraper to divide the dough into 8 equal pieces.
Melt the remaining 1/4 cup butter in a 9-inch cast iron skillet over medium heat. Place the biscuits in the pan and then turn them over, so the butter side is up.