Preheat oven to 500 degrees F (260 degrees C).

Combine ponzu sauce, 1 cup cilantro, pineapple juice, mint leaves, garlic, fresh ginger, sesame oil, chili oil, and brown sugar together in a large bowl. Add chicken and toss to coat.

Remove chicken from ponzu sauce mixture, reserving marinade. Heat large pot or Dutch oven over medium-high heat. Add chicken and cook, stirring frequently, until browned, about 5 minutes. Stir in olive oil, onion, red bell pepper, jalapeno pepper, salt, and black pepper. Cook and stir until onion has softened and turned translucent, about 5 minutes.

Pour reserved marinade into chicken mixture and bring to a boil. Stir in cabbage and cook until slightly wilted, 4 to 5 minutes.

Using a slotted spoon, transfer chicken mixture into toasted hoagie buns and top each sandwich with 3 slices Swiss cheese.

Place sandwiches onto a baking sheet and bake in the preheated oven until cheese is melted and buns are toasted, about 5 minutes. Garnish each sandwich with 2 tablespoons cilantro, 1/4 of the sesame seeds, and 1/4 of the chile-garlic sauce. Serve with lime wedges.