Mix black pepper and smoked paprika together in a bowl; season 1 side of each chicken breast with black pepper mixture. Flip each chicken breast over and season the other side with about 1 1/2 teaspoons ground chipotle per chicken breast. Wrap chicken breasts in plastic wrap and refrigerate 8 hours to overnight.
Bring a pot of water to a boil; add vegetable bouillon and rosemary. Stir carrots, mushrooms, celery, and garlic into boiling broth; cook until vegetables are tender, about 10 minutes. Strain vegetables from broth using a slotted spoon and transfer to a bowl.
Preheat the grill to 300 degrees F (150 degrees C). Soak 8 toothpicks in a bowl of water.
Remove plastic wrap from chicken breasts and place chipotle-side down on a work surface. Spoon the vegetable mixture onto each chicken breast; roll chicken breast around filling. Secure each breast with 2 toothpicks. Season outside of rolls with more ground chipotle.
Grill chicken breasts until no longer pink in the center and the juices run clear, about 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Brush chicken breasts with barbeque sauce; cook until exterior is caramelized, about 10 more minutes.
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