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When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 375F and preheat, lid closed, for 10 to 15 minutes.
Lightly sprinkle the chicken breasts with the taco seasoning. Arrange directly on the grill grate and grill, turning once, until the internal temperature is 165F, about 25 to 30 minutes. Leave the grill on. Let the chicken cool slightly, then dice.
Stem and seed the bell pepper, then dice or cut into very thin strips.
Pour the melted butter on a rimmed baking sheet to barely coat. Lay the tortillas side by side in the butter. Press down gently to make sure the bottom sides of the tortillas are uniformly coated.
Brush the top of each tortilla with the barbecue sauce. Top 1/2 of each tortilla with some of the cheese, chicken, and bell pepper. Add any optional toppings, then sprinkle with more cheese. Fold the tortilla in half over the toppings.
Transfer the baking sheet with the quesadillas to the grill grate. Grill for 8 to 10 minutes, or until the underside is lightly browned and the cheese has melted. Carefully flip the tortillas with a wide spatula and continue to cook the other sides until they are lightly browned, 6 to 8 minutes more.
Use a pizza cutter or knife to cut each quesadilla into wedges. Serve with guacamole, sour cream, and/or pico de gallo.
Recipes for grilling and smoking turkey, cooking grilled chicken, steak, bacon, brisket, salmon, vegetables and everything in between. Best smoked recipes for your grill.