How to Make It
Prepare the Biscuits: Preheat oven to 475°F. Grate frozen butter using large holes of a box grater. Toss together grated butter, self-rising flour, chives, and salt in a medium bowl. Chill 10 minutes.
Make a well in center of flour mixture. Add buttermilk, and stir 15 times. (Dough will be sticky.) Turn dough out onto a lightly floured surface. Lightly sprinkle additional flour over top of dough. Using a lightly floured rolling pin, roll dough to a 3/4-inch-thick rectangle (about 9 x 5 inches). Fold dough in half so short ends meet. Repeat rolling and folding process 4 more times.
Roll dough to 1/2-inch thickness. Cut with a lightly floured 2 1/2-inch round cutter, rerolling scraps as needed.
Place dough rounds on a rimmed baking sheet lined with parchment paper. Bake in preheated oven until lightly browned, about 15 minutes. Brush hot biscuits with melted butter.
Prepare the Beef: Whisk together buttermilk and egg in a medium bowl. Stir together flour, salt, and black pepper in a shallow bowl. Dip Beef slices in buttermilk mixture; dredge in flour mixture, shaking off any excess.
Heat canola oil in a large skillet over medium-high until hot. Fry Beef slices, in 2 batches, in hot oil until golden brown, 2 to 3 minutes per side. Drain on a wire rack over a rimmed baking sheet.
Split biscuits in half. Spread 1 to 2 teaspoons Mustard Sauce on bottom half of each biscuit; top evenly with Beef slices and 1 to 2 teaspoons Mustard Sauce. Sprinkle with scallions and parsley; cover with top halves of biscuits, and serve immediately.