For the chicken fried steak: Cut the cube steak into eighteen 2- to 3-ounce portions and put into a bowl. Pour over the buttermilk, toss to cover and marinate for 1 hour.
Add the all-purpose flour, pepper, seasoning salt, paprika and cayenne to a shallow dish and mix. Whisk the milk and eggs in a separate dish.
Remove the steaks from the buttermilk with tongs, shaking off as much excess liquid as possible. Dredge portions in the dry mixture first, then quickly add to the egg mixture, then back to the dry mix (dry/wet/dry). Place the breaded steaks on a baking sheet and repeat until all portions are breaded. (You can cover and refrigerate at this stage until ready to fry.)
Heat the vegetable oil and butter in a large cast-iron skillet over medium to medium-high heat. Fry the steaks 4 or 5 at a time, flipping them midway through, until golden brown, 2 to 3 minutes per side. Transfer to a paper towel-lined baking sheet. Cover the steaks loosely with foil to keep warm.
For the buttermilk biscuits: Preheat the oven to 350 degrees F.
Grate the unsalted butter using the large grate of a box grater and place in the freezer for 2 to 3 minutes. In the bowl of an electric mixer fitted with a paddle attachment, add the self-rising flour, sugar, baking powder and salt and mix until combined. Add the grated butter and blend until the mixture is well combined and the butter is in about pea-size chunks. Slowly add in the buttermilk and heavy cream and mix until the dough comes together.
Turn out onto a floured surface, use your hands to form into a rough rectangle and roll out to 3/4 inch thick. If the dough is still tacky, work in an additional 2 tablespoons self-rising flour to the dough. Dip the cutting edge of a 2 1/2-inch round biscuit cutter into some flour, then cut out as many biscuits as possible. Gather the remaining dough, reroll to 3/4 inch and cut out additional biscuits until you have 18. Split the biscuits into 2 separate 14-inch cast-iron skillets, brush the tops with the melted salted butter and bake until golden, 25 to 30 minutes.
For the gravy: Into a glass measuring cup, pour off all the grease from the skillet where the steaks were fried. Add 1 cup of the grease back into the skillet over medium-high heat. Sprinkle on the all-purpose flour in 3 batches. Whisk the mixture until it becomes a paste. Whisking constantly, gradually pour in the milk and buttermilk. Add the salt, pepper and more milk if it seems too thick. Allow the gravy to cook and thicken.
Lay out the biscuits, steaks and gravy for the sliders and have everyone help themselves. Serve with sliced tomatoes and fried potatoes.