Preheat the oven to 350 F.
Make the chicken: Pat the chicken thighs dry and season generously with salt and pepper.
In a large skillet, heat 1 tablespoon of olive oil over medium-high heat. Add the chicken thighs skin side down and cook without moving, until the skin is a deep golden brown and releases with ease from the bottom of the pan, 8 to 10 minutes.
Once the skin is browned, flip the chicken and brown the other side, about 5 minutes. Transfer the chicken to a plate.
Add the cabbage and sliced onion to the pan and season with salt and pepper. Cook, stirring occasionally, until the vegetables begin to release moisture and soften slightly. Deglaze with 1 cup chicken stock and scrape up any browned bits on the bottom of the skillet. Bring to a boil and reduce slightly to concentrate flavors, 3 to 4 minutes.
Nestle the chicken thighs back into the skillet with any accumulated juices and place the skillet in the oven for 25 to 30 minutes, or until the chicken is supremely tender and the cabbage is soft.
Make the scallion-ginger sauce: In a mortar and pestle, mash together the scallions, cilantro, ginger, garlic, habanero, allspice, and vinegar. Season the sauce generously with salt and pepper, and stream in the olive oil while mashing to thoroughly incorporate.
To serve: Arrange the chicken thighs on a platter with pan drippings, cabbage, and onions, and spoon the green sauce over top.