In a medium plastic resealable bag, combine the flour, garlic powder, and onion powder. Add the beef and shake the bag until the beef is evenly coated with the flour mixture. Let the beef rest for 15 minutes, unrefrigerated (though not longer, for food safety reasons).

Preheat a medium nonstick soup pot over medium high heat. When it's hot, lightly mist the pan with spray then add the beef. Brown the beef on all sides, about 1 minute per side, then turn the heat to medium and add the broth and liquid smoke. When the liquid comes to a boil, reduce the heat to low (the liquid should still be boiling slightly). Cover and cook the beef, stirring occasionally, for 1 to 1 1/2 hours or until it's very tender (the pieces should easily fall apart when smashed with a fork).

Using a slotted spoon, drain the beef of any excess liquid and transfer it to a medium bowl. Using a fork, separate the pieces so the beef is somewhat shredded then mix in 1/4 cup of the barbecue sauce.