Make the Tortilla Dough
In a large bowl, stir together the sourdough discard, olive oil, and water until smooth. Add the flour and salt, mixing until a soft dough forms. Knead briefly, about 1 to 2 minutes, until no dry spots remain. Cover with a damp towel and let rest at room temperature for 30 minutes.
Prepare the Burger Sauce
In a small bowl, mix the mayonnaise, paprika, onion powder, garlic powder, mustard, minced pickles, pickle brine, honey, Worcestershire-style sauce, and black pepper until fully combined. Cover and refrigerate until ready to use.
Cook the Tortillas
Heat a large skillet over medium-high heat. Divide the rested dough into 10 equal pieces. Roll each piece into a thin circle, about ⅛-inch thick. Cook in the dry skillet for about 1 minute per side, until bubbles form and light golden spots appear. Stack the cooked tortillas and keep warm.
Prepare the Beef
Divide the ground beef into 4 equal portions. Gently roll into loose balls and season lightly with salt and black pepper.
Smash and Cook
Heat a heavy skillet over high heat until very hot. Place a beef ball in the pan and immediately lay one tortilla on top. Press down firmly with a spatula until the beef spreads thin beneath the tortilla. Cook for about 3 minutes, until the beef is well browned and crisp.
Flip and Melt the Cheese
Flip so the beef side faces up. Reduce heat to medium, sprinkle generously with shredded cheddar, cover, and cook for 1 to 2 minutes until the cheese melts and the tortilla is heated through.
Assemble and Serve
Transfer to a plate and top with shredded cabbage, sliced pickles, and a generous drizzle of burger sauce. Serve immediately while hot and crispy.
