The trick is to smoke the meat and not make the meat smoke

SLOPPY JOES

  Date: May 13, 2007
  Favorite: Sandwiches
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  Info
This recipe from Weber’s Big Book of Grilling is called Too Good to be True Sloppy Joes. While it lives up to it’s name, you’d better like Sloppy Joes because it is about a 4 hour cook from start to finish. The meat is a Chuck Roast seared and an indirect grilled for 2 hours. I made the sauce on the side burner, This makes a very subtle yet spicy Sloppy Joes and was worth the wait.
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  Recipe Source:
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Meathead
Weber's Big Book of Grilling:
Too Good to be True Sloppy Joes - Page 127
  Grill:
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Kenmore Elite Gas Grill
Direct Grilled:
Using Kenmore Elite Gas Grill
  Gear:
  • SR 19" Locking Tongs