Halve the leeks lengthwise and slice into half rings. Rinse thoroughly under cold water to remove dirt. Cut the avocados in half, remove the pits, and slice the flesh into long strips. Mince the chilies and set aside.
Drain and rinse the jackfruit. Cut into bite-sized pieces (about ¾ inch). Drain and rinse the black beans.
Heat 2 tablespoons of oil in a large skillet over medium heat. Add the leeks, jackfruit, and a pinch of salt. Sauté for 5–7 minutes, stirring frequently, until softened.
Add the smoked paprika, sweet paprika, garlic powder, and lemon juice. Cook for 2 minutes, allowing the spices to become fragrant.
Stir in the black beans, coconut cream, and soy sauce. Reduce heat slightly and simmer for 5–7 minutes, stirring often, until the mixture thickens into a creamy filling. Taste and season with more salt if needed.
Place one pita on a clean work surface. Spoon a generous portion of the jackfruit mixture onto one half of the wrap. Top with avocado slices and a sprinkle of minced chili.
Fold the pita in half over the filling to form a semicircle.
Heat a dry skillet over medium heat. Place the wrap in the pan and toast for 1–2 minutes per side, pressing down gently, until golden and crispy. Repeat with remaining wraps.
Slice the wraps in half and serve warm.