Slaw
Ground Steak
For the slaw Whisk mayonnaise, sugar, vinegar, salt, and pepper together in bowl. Add cabbage and toss to coat; refrigerate until ready to use.
For the ground steak Cook beef, pepper, and salt in 12-inch cast-iron skillet over medium heat, breaking up meat with wooden spoon, until beef is no longer pink, 7 to 10 minutes. Mash beef with potato masher until fine-textured, about 1 minute.
Sprinkle flour over beef and cook, stirring constantly, until flour has been absorbed, about 1 minute. Slowly stir in water and cook, scraping up any flour sticking to skillet, until mixture has thickened and becomes cohesive, 2 to 4 minutes.
Spread mayonnaise evenly on bun bottoms. Divide beef mixture among bun bottoms, then top with tomato slices, coleslaw, and bun tops. Serve.