Drain and rinse jackfruit. Cut off the center “core” portion of each piece. Squeeze jackfruit with hands to remove excess water. Pat dry with paper towels and place in a large mixing bowl.
Use hands or potato masher to smush and separate jackfruit in bowl. Add sugar and spices and toss to combine.
Heat 1 or 2 tablespoons vegetable oil in a skillet on medium-high heat. Add jackfruit and toss to coat with oil. Cook, stir-fry style, for 4 or 5 minutes until jackfruit begin to brown. Stir in BBQ sauce. If sauce is too thick, thin with water.
Turn down heat. Cover and cook for 25 minutes, stirring occasionally.
Remove cover and increase heat. Add molasses and liquid smoke. Cook for an additional 5 minutes, stirring constantly.
Remove from heat. Serve hot on a bun with additional sauce.
(Inspired by Blissful Basil and Minimalist Baker)