Arrange beef on tortilla. Drizzle with barbecue sauce and top with cheese and broccoli. Roll up. Wrap tightly in plastic wrap and chill for up to 24 hours.
Assemble sandwich the night before, wrap in plastic wrap, and chill. Tote in an insulated container with ice packs; refrigerate within 1 hour. Hold in the refrigerator for up to 5 hours.