Preheat an electric griddle or fry pan to medium-high, about 350 degrees F (175 degrees C). Stir the flour, salt, baking powder, and baking soda together in a large bowl until well combined.
Stir in the buttermilk, 1/2 cup at a time, until the mixture forms a very sticky ball of dough. Turn the dough out onto a well-floured surface, and knead gently 8 to 10 times. Pat the dough into a circle about 1 1/2 inch thick, and cut the circle into quarters.
Place the wedges onto the preheated griddle and cook until the bottom is golden brown, about 15 minutes; turn over and cook the other side until golden, another 10 to 15 minutes. A toothpick inserted into the center of a wedge should come out clean. Stand the wedges on a wire rack to cool, then cut each wedge in half and slice horizontally for serving.
