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1
Make the rub: in a small bowl, mix together the rub ingredients.
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2
Press the rub into the roast and allow to stand at room temperature for 20-30 minutes before grilling.
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3
Lightly brush or spray the roast with olive oil; sear on grill over direct medium heat for 15 minutes, turning once halfway through searing time.
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4
Continue grilling over indirect medium heat until the internal temperature reaches 160, 1 to 1 1/2 hours.
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5
Remove from grill and let rest for 15-20 minutes.
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6
Make the sauce: in a saucepan over med-high heat, warm the oil.
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7
Add in the onion and bell pepper; cook/stir 8-10 minutes, until the onion is soft and lightly browned.
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8
Add in garlic; cook/stir for 1 minute; sprinkle in the flour and chili powder; stir to combine.
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9
Add in beef broth; bring to a boil over high heat, whisking occasionally.
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10
Add in the tomatoes and barbecue sauce; stir to combine.
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11
Decrease the heat and simmer, stirring occasionally, until mixture is the consistency of gravy, about 30 minutes.
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12
Using a sharp knife, chop the meat into 1/4-inch pieces or matchstick-size strips.
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13
Add to the sauce and simmer for 10-15 minutes to let the flavors fully incorporate.
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14
Season to taste with salt and pepper; if sauce seems too thick, add 1/4 cup water.
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15
Grill the buns over direct medium heat until lightly toasted, about 30 seconds.
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16
Spoon the beef mixture onto the buns and serve; they dont call it sloppy for nothing.
