Heat the olive oil over medium-high heat in a skillet. Add onion and saute until it begins turning brown, about 10 to 15 minutes. Add the garlic and saute until fragrant, about 2 minutes. Add the remaining ingredients for the sauce and bring to a full boil. Reduce the heat to a simmer and cook un-covered for 20 to 30 minutes, until sauce has thickened. Transfer sauce to a blender and blend until smooth. As the sauce sits, it will thicken more. Transfer to a large jar and refrigerate until ready to use.
Prepare Jackfruit Sandwiches:
Drain and rinse the cans of jackfruit. Use a fork to “pull” it like pulled pork, removing and discarding any dark or hard pieces and the small "bulbs" that look like garlic.
Heat a small skillet to medium and add enough olive oil to generously coat the surface. Transfer the jackfruit to the hot skillet and cook 2 to 3 minutes, stirring occasionally, until jackfruit is somewhat crispy. Add the barbecue sauce and bring the mixture to a gentle boil. Reduce the heat and simmer and cook 10 minutes, adding more sauce if necessary. Taste the mixture for flavor and add more sauce and/or sea salt to taste.
Add the cabbage, lime juice, olive oil, garlic, and sea salt to a mixing bowl. Stir well to combine so that all of the cabbage is coated in olive oil and lime juice. Set aside until ready to use (Note: this part of the recipe can be prepared up to 2 days ahead of time).
Toast the buns and add desired amount of BBQ jackfruit, cabbage slaw, avocado, and sliced peaches. Serve alongside your favorite side dish(es).