Preheat the oven to 375 degrees F.
Coat a 13x9-inch baking pan with nonstick cooking spray.
In a large bowl, whisk the barbeque sauce and the enchilada sauce together.
Place the chicken in the prepared pan and drizzle with 1/4 cup of the barbeque mixture.
Bake, uncovered, until the chicken juices run clear, an instant thermometer inserted in the center reads 165 degrees F, and the meat is no longer pink, about 20-25 minutes.
Allow the cooked chicken to cool and then chop or shred it.
While the chicken is cooking, in a large skillet over medium-high heat, heat the olive oil.
Add the garlic to the oil and cook until golden and fragrant, about 1 minute.
Add the red onion to the garlic and cook until the onion is translucent, about 3-5 minutes.
Transfer the veggie mixture away from the heat and immediately add 1 cup of the barbeque mixture and the sweet potatoes.
Add the shredded chicken, the cumin, and the cilantro to the veggie mixture, stirring until just combined.
In a bowl, combine the Mexican blend cheese and the mozzarella cheese.
Place 1/4 cup of the barbeque mixture in the bottom of a 9-inch baking pan.
Dip 3 of the tortillas in the barbeque mixture and place at the bottom of the pan. You may need to cut 1 of the tortillas in half to ensure it covers the entire surface.
Place 1/2 of the chicken mixture on top of the barbeque mixture-coated tortillas, cover with 1/2 cup of the cheese mixture, and about 1/4 cup of the barbeque mixture.
Repeat the layers once, starting with the barbeque mixture and ending with the cheese mixture.
Bake, covered with foil, until warmed through and the cheese is melted, about 30-40 minutes.
Allow the casserole to cool, about 5-10 minutes, then garnish with the cilantro.
Serve.