Heat oven to 425°F. Place 1 1/2 pounds boneless, skinless chicken thighs on a large sheet pan with the zest and juice of 1 lime, 1 tablespoon of the olive oil and season well with salt and pepper. Push to one side of the sheet pan. Add 1 pound tomatillos, 1/2 onion, 2 cloves garlic, and a jalapeño to the other side.
Roast in the oven until chicken is cooked all the way through and vegetables are tender, about 25-30 minutes. Stick under the broiler for a few minutes to brown the chicken and char the vegetables. DON’T turn the broiler off.
While everything is roasting, combine 2 cups shredded red cabbage, 1 cup shredded green cabbage and an 1/8 of a red onion, sliced thin in a medium bowl. Toss with lime juice from ½ a lime, the remaining 2 tablespoons of olive oil and salt to taste. Taste and add more lime juice or salt if needed.
Remove the skin from the garlic then transfer roasted vegetables to a blender with 1 bunch cilantro and 1/2 teaspoon salt. Blend until smooth. Taste and add more salt if needed.
Shred chicken and return to the sheet pan. Pour sauce over chicken (you won’t use all the sauce), toss to coat and stick back under the broiler for a couple minutes to rewarm and crisp the edges.
Serve in warm tortillas with slaw, sour cream, and avocado.