Preheat your oven to 425°F (220°C) and place a large rimmed baking sheet inside to get hot.
Slice the green cabbage into thick wedges, keeping the core intact so they stay together.
In a large bowl, toss the cabbage wedges and chicken breast with the extra virgin olive oil, garlic powder, sea salt, and black pepper until evenly coated.
Carefully remove the hot baking sheet from the oven and arrange the cabbage and chicken in a single layer.
Roast for 20-25 minutes, flipping the chicken and cabbage halfway through, until the cabbage edges are deeply charred and the chicken is cooked through.
While roasting, whisk together the plain Greek yogurt, fresh lemon juice, and dried oregano in a small bowl to create the dressing.
Slice the roasted chicken into strips and serve over the charred cabbage wedges.
Drizzle the lemon-herb dressing over the top and garnish with freshly chopped parsley.