Place the cabbage in a large bowl. Cover with cool water and stir in a pinch of salt. Set aside for 20 minutes, then strain well and set in a large bowl.

Prepare a bowl of ice water. Rub the chicken with olive oil and season with salt and pepper. Set on a hot grill and cook until charred and cooked through, about 3 minutes per side. Transfer the chicken to the bowl of ice water, and set aside for at least 5 minutes to cool. When cool, remove from water and use two forks to shred the chicken. Transfer the shredded chicken to the bowl of cabbage, and set aside.

In a large skillet over medium-high heat, add the avocado oil. When hot, add the shallot and saute for 2-3 minutes, until translucent. Stir in the garlic and saute another 2 minutes, until golden. Strain the garlic and shallots into a fine mesh strainer, collecting the avocado oil in a bowl underneath. Set the oil aside to cool, about 5 minutes. Reserve the shallots and garlic.

When the oil is cool, whisk in the lime juice, fish sauce, salt, pepper, honey and apple cider vinegar. Taste the dressing and add more salt if needed. 

Add the julienned green pepper, chile pepper, cilantro and mint to the bowl of chicken and cabbage. Cover with the dressing, and toss to combine. Taste and add salt to taste.  Serve topped with the fried shallots and garlic.