Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Slice the green cabbage into 1-inch thick wedges, ensuring the core remains intact to hold the leaves together.
Place the cabbage wedges and chicken breast on the prepared baking sheet, then brush both sides with half of the olive oil.
Season the chicken and cabbage wedges evenly with sea salt, black pepper, and dried oregano.
Roast in the oven for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the cabbage edges are beautifully charred.
While the tray is roasting, whisk together the remaining olive oil, lemon juice, lemon zest, minced garlic, and finely chopped parsley in a small bowl.
Remove the tray from the oven, slice the chicken into strips, and drizzle the vibrant lemon-herb dressing over the warm roasted components before serving.