How to Make It
In a bowl, whisk the mayonnaise, vinegar and sugar and season with salt and pepper. In a food processor, pulse the coleslaw until coarsely chopped. Stir the slaw into the dressing and let stand for 10 minutes.
In a large saucepan, combine the remaining glaze and the broth and simmer over moderate heat until reduced by half, about 5 minutes. Add the chopped steak, season with salt and pepper and cook until just heated through, about 2 minutes.
Top the brioche buns with the lettuce and tomato and mound the steak on top. Using a slotted spoon, cover with the coleslaw. Close the Sloppy Joes and serve.