Preheat the oven to 425 degrees. Place 2 tablespoons of butter into a 12 to 15-inch cast iron skillet. Put The skillet in the oven until the butter is melted.
Whisk together the eggs in buttermilk.
In a large bowl or food processor, combine the flour, baking powder, cream of tartar, and salt. Cut in the remaining butter until the mixture is sandy.
Combine the flour mixture with the buttermilk mixture until it comes together in a large ball.
Turn the dough out onto a lightly floured surface. Fold the dough over 6 to 8 times. (The more times the dough is folded, the more layers the biscuits will have.) Pat into a large rectangle, about ½ inch thick. use a biscuit cutter to cut 12 to 15 biscuits from the dough, reshaping the dough as needed.
Transfer the biscuits to the prepared skillet.
Place in the oven and bake for 15 to 20 minutes.
If desired, brush with melted butter before serving.