For the biscuits: Preheat oven to 350°. Grease a baking sheet with shortening and set aside. Sift flour, baking powder, salt, and sugar into a large bowl. Add cheese, scallions, and cream, stirring until dough just comes together. Turn dough out onto a floured surface and quickly knead 8–10 times. Roll dough out to a 1⁄2"-thick 6" × 8" rectangle and, using a 2" round cookie cutter, cut out 12 biscuits. Put biscuits on prepared baking sheet. Bake until golden brown, turning baking sheet, if necessary, to brown biscuits evenly, 20–25 minutes.
For the steak: Preheat oven to 200°. Put 1 1⁄2 cups of the flour into a wide shallow dish. Season flour with salt and 1⁄2 tsp. of the black pepper and set aside. Put eggs, cream, and 1⁄2 cup of the milk into another wide shallow dish, beat well, and set aside. Heat oil and bacon grease together in a large cast-iron skillet over medium heat until hot or about 360° on a candy thermometer. Meanwhile, working with 4 pieces of meat at a time, lightly season both sides with salt and pepper. Dredge beef in seasoned flour, shaking off excess, then dip each side into egg mixture. Dredge in flour again, shaking off excess. Fry meat in the hot fat, turning once, until dark golden brown on each side, about 2 minutes per side. Transfer to a wire rack set over a baking sheet and keep warm in oven. Repeat seasoning and cooking process with remaining meat and flour and egg mixtures, transferring meat to oven as done.
Discard all but 3 tbsp. of the fat from the skillet and heat over medium heat. Add remaining 3 tbsp. flour and cook, whisking constantly, until golden, about 2 minutes. Gradually whisk in stock, remaining 1 1⁄2 cups milk, worcestershire, Tabasco, garlic, cayenne, and remaining 1⁄2 tsp. black pepper. Season to taste with salt; simmer, stirring, until thickened, about 5 minutes.
To assemble biscuits, slit them crosswise three-quarters of the way through. Spread some butter on the bottom half of each. Stuff each biscuit with a piece of steak, spoon on some gravy, and close biscuit.