Cut the non-shreddable inner core from the jackfruit and chop it finely along with any seed pods. Shred outer portion of jackfruit by hand and add to a bowl with chopped core and seed pods. Add oil, half the orange juice, cumin, oregano, salt, pepper, and cayenne and toss to combine.
Heat a large skillet over medium. Add the jackfruit mixture and press into an even layer with a spatula. When browned, stir and press into an even layer again. Repeat a few times until all of jackfruit is evenly browned. Remove from heat and stir in remaining orange juice.