Prepare oven and baking sheet: Preheat oven to 375°F. Line a baking sheet with foil.
Mix filling: Combine scallions, cream cheese, cheddar, and garlic in a large bowl, stirring until well combined. Add brisket and stir well to combine. Set aside.
Prepare peppers: Wear gloves for pepper prep. Cut a lengthwise slit all the way down one side of each pepper. Cut a crosswise slit at the top of the pepper near the stem, making sure not to cut all the way through (you want to keep the stem on, as it helps keep the filling from leaking out). Carefully open each pepper and scrape out the seeds and membranes; the small side of a melon baller works well for this.
Assemble peppers: Divide filling evenly among prepared peppers and arrange on prepared pan. Stretch each bacon slice by tugging gently to elongate; wrap 1 bacon slice around each stuffed pepper. Secure ends with toothpicks.
Bake peppers: Bake at 375°F until filling is thoroughly heated and peppers are tender when pierced with a knife.
Add barbecue sauce: Remove pan from oven and preheat broiler to High. Brush barbecue sauce over tops of peppers; broil until browned, 1 to 2 minutes. Carefully turn peppers over and brush with more sauce; broil 1 to 2 minutes.
