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.
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Review Body: It may be good if you gave the complete instructions. Like 1) marinating the steak over night with what? 2) You said to add the remaining glaze, where did the other glaze go to? 3) Do we grill the steak ahead of adding or it only takes 2 minutes for it to cook after adding to the "remaining glaze"?