For the chicken and marinade: Gently press each thigh between 2 pieces of plastic wrap to flatten (do this with a rolling pin, it's less brutal than pounding). Season the chicken on both sides with salt and pepper. Place the chicken in a large resealable plastic bag with the oil, cumin and lime zest and juice. Seal the bag and squish everything around until everything is coated by everything. Rest on the counter for 1 hour.
For the spread: In a medium bowl, add the cilantro, bacon, avocado, tomatoes and hot sauce if using. Fold to combine gently so the tomatoes don't get mashed, then taste and season with a pinch of salt if needed. Cover by placing plastic wrap directly on the top of the spread and refrigerate until using.
For the caramelized onions: In a large pot on low heat (or in a pot over the indirect heat area of a grill), add the onions, olive oil, butter, a pinch of salt and a few grinds of pepper. Cook, stirring every other minute or so, until the onions are tender and a deep golden brown, about 30 minutes.
Preheat a grill or grill pan to medium-high heat.
Remove the chicken from the bag, shaking off excess marinade. Place the chicken over the direct heat of the grill (or on the grill pan). Once the chicken releases from the grill and can be flipped, flip it to the indirect heat side of the grill (or lower the heat on the grill pan) and grill until cooked through, just 3 to 4 minutes more. Remove the chicken to a cutting board and cover with aluminum foil for 10 minutes. Roughly chop the chicken.
To assemble and serve. Build each burger in this order, starting at the bottom with: the bottom bun, slice of cheese, big scoop of chicken and caramelized onions and the top roll slathered with tons of avocado spread.