Prepare the jackfruit: drain the cans of jackfruit and rinse well.
Cook the onion: in a large skillet over medium-high heat, add 1 tbsp olive oil. Once hot, add the diced onion. Saute for 3 - 4 minutes, until translucent.
Cook the jackfruit: add the jackfruit and ¾ cup BBQ sauce to the skillet. Pour in ⅓ cup of water and stir. Cover skillet and simmer 15 - 20 minutes, stirring occasionally.
Shred the jackfruit: using 2 forks or a potato masher, shred the jackfruit into bite-sized pieces. Sprinkle generously with pepper to taste.
Turn up heat: turn up the heat to medium-high and cook for 5 minutes, uncovered, stirring frequently.
Add more BBQ sauce: remove the pan from the heat and stir in remaining ¼ cup BBQ sauce.
Serve: serve on hamburger buns, optionally topped with coleslaw or lettuce & tomato.