Add chicken, 1/2 cup panko bread crumbs, 2 eggs, oregano, cumin, salt and pepper to a food processor. Pulse several times, until chicken is broken down and ingredients are mixed.

Use a paper towel to remove any excessive water from the green chile. Add green chile to chicken mixture, and stir well. If mixture is too wet, add in some extra breadcrumbs. Form the mixture into balls about the size of a golf ball. Grab a piece of cheese and press into the center of the ball, then fold the chicken mixture around the cheese and reform into a ball.

In a small bowl, whisk the remaining egg. Add 1/2 cup panko breadcrumbs to another bowl. Dip each green chile ball into the egg, then roll in breadcrumbs and set aside on a plate. Repeat until all green chile balls are breaded.

Place the balls into the freezer for 10 minutes. Meanwhile, heat 2 - 3" of oil in a pan over medium heat.

Remove green chile balls from the freezer, and fry in batches until golden brown, about 3 - 5 minutes per batch.