Lightly dust the quartered rabbit with kosher salt and freshly cracked black pepper. Grill over an open flame or sear in a hot skillet. Be sure to sear all sides evenly.
Once seared, add to the slow cooker and set to low. Add freshly minced garlic, Coca-Cola, BBQ sauce, chicken stock, and freshly squeezed lime juice.
Make sure the rabbit quarters are at least half-covered by the liquid and secure the lid in place.
In a skillet heated on medium-low, add a little bit of olive oil and the finely diced red onion. Lightly season with salt and pepper and cook until caramelized, stirring often and being careful not to burn. This should take about a half hour to accomplish.
Add the caramelized red onion to the slow cooker and stir in with the rabbit.
Make sure that the liquids mostly cover the rabbit to prevent the meat from drying out. Braise for at least 8 hours on low, until the meat falls off the bone. If more liquid is required, add in equal parts of BBQ sauce and chicken stock.
Once the meat is tender, make certain to remove all of the bones.
To serve, separate and wash the lettuce. Shred the rabbit meat. Place the shredded rabbit on individual leaves, topping with shredded mozzarella and freshly minced cilantro.