Heat the oil in a large skillet over medium-high heat. Reserve ¼ cup onion for garnish and add the rest to the pan. Cook, stirring occasionally, until softened, about 5 minutes. Add the garlic and cook, stirring, for 30 seconds. Add the jackfruit and smash with the back of a spoon or potato masher. Add the cumin, oregano, salt, and pepper, and stir. Cook, stirring occasionally, until the jackfruit starts to sear, about 10 minutes. Add the green chilies, chipotle pepper, vegetable broth, vinegar, and lime juice. Stir well and bring to a simmer. Reduce heat and continue to cook, stirring occasionally, until all the liquid has evaporated, about 10 minutes.
Combine the reserved onion with the cilantro and serve the jackfruit mixture in tortillas with the cilantro/onion garnish and sliced radishes.