Prepare the chicken: In a bowl, combine the chicken, barbecue sauce, lime juice, olive oil, balsamic, Worcestershire sauce, garlic, cumin, smoked paprika, and salt. Stir to combine. Set aside for at least 15 minutes, or refrigerate for a few hours or overnight.
Cook the chicken: Preheat the oven to 425 F. Place the marinated chicken on a large rimmed baking sheet and bake for 15-20 minutes, or until cooked through and no longer pink inside. Broil for 1 minute at the end.
Roast the vegetables: Arrange the vegetables on a large rimmed baking sheet. Drizzle with the oil and sprinkle with the basil, red pepper flakes, salt, and pepper. Toss to coat. Roast for 15-20 minutes at 425 F.
Make the goddess sauce: Combine the lime juice, pepitas, basil, garlic salt, pepper, and water in a blender. Blend until smooth.
Make the sandwiches: Slice the buns in half and toast if desired. Spread some goddess sauce on the bottom half, then top with the chicken, roasted vegetables, cheese, tomato, and lettuce. Enjoy!
Note: If you have a barbecue, you can marinate whole or half chicken breasts and cook them on the barbecue.