Preheat to 400°F.

Pat the chicken very dry with paper towel and season both sides with ½ teaspoon kosher salt and ¼ teaspoon freshly-cracked black pepper.

Preheat an oven-safe skillet over medium heat. Add the olive oil and heat it until shimmering. Carefully add the chicken, skin-side down, and cook, undisturbed, until the skin is golden brown and crispy, around 6 minutes. Reserve 2 tablespoons of the pan drippings, transfer the chicken to a tray, skin-side up, and set it aside.

Carefully add the cabbage to the pan, one of the cut sides down, and cook, undisturbed, until deeply browned, around 3 minutes. If the pan drippings are absorbed, add more olive oil to coat the bottom of the pan. Flip the cabbage and cook the other cut sides until deeply browned, around 3 more minutes. Transfer the cabbage to the tray with the chicken, browned sides up, and set it aside.

Add the water and use a spoon to lift any brown bits. Bring the liquid to a simmer, add the butter, paprika and thyme and stir until melted and emulsified. Add the mustard and stir until emulsified. Taste the sauce for seasoning and adjust with salt and pepper as desired. Return the cabbage to the pan, browned sides up, and nestle the chicken thighs in between, skin-side up. Transfer skillet to the oven and roast until the thickest part of the chicken registers 180°F and the cabbage is fork-tender, around 20 minutes. Optionally, switch the oven to broil and cook for an extra 2 to 3 minutes for extra crispy chicken skin and cabbage.

Serve the pan-roasted chicken and cabbage with a side of steamed rice, mashed potatoes or green salad.