Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Slice the purple cabbage into 1-inch thick wedges, keeping the core intact so the leaves stay together during roasting.
In a small glass bowl, whisk together the olive oil, honey, Dijon mustard, apple cider vinegar, sea salt, and black pepper until smooth.
Place the chicken breast and cabbage wedges on the prepared baking sheet, ensuring they are in a single layer without overcrowding.
Brush the honey-mustard glaze generously over both sides of the chicken and the cabbage wedges using a pastry brush.
Roast for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the cabbage edges are crispy and caramelized.
Remove from the oven and let the chicken rest for 5 minutes before slicing, then garnish everything with fresh thyme leaves.