Preheat oven to 425 degrees F (220 degrees C). Grease an 8-inch cast-iron skillet with shortening.

In a large mixing bowl or the bowl of a food processor, sift together flour, sugar, baking powder, salt, and cream of tartar. Mix or pulse a few times to combine.

Cut butter and 1/4 cup shortening into flour mixture just until you get a crumbly consistency. Add buttermilk to flour mixture. Gently stir until just combined, being careful not to overmix.

Turn out dough onto a floured surface. With floured hands, pat dough to approximately 2-inch thickness. Using a 2 1/2-inch biscuit cutter, cut out 6 to 8 biscuits. Transfer to greased skillet.

Bake until golden brown, about 30 minutes. Remove biscuits from oven and let cool 5 minutes.

While biscuits are baking, cook ham: Add bacon grease to a cast-iron skillet over medium heat. Add ham slices and fry until edges are brown, a few minutes per side. Remove ham from skillet and place on a paper towel–lined plate to drain.