Preheat the oven to 425°F (220°C).

Chop the green cabbage into 1-inch pieces and place it on the large sheet pan.

Drizzle the cabbage with 2 1/2 tbsp olive oil and season with 3/4 tsp salt and 1/2 tsp black pepper.

Roast the cabbage for 25 to 30 minutes, tossing it a couple of times, until browned and tender.

Heat a little olive oil in the skillet over medium-high heat and place the lemon half cut-side down.

Char the lemon for 2 minutes, then remove it from the skillet.

Add 3 tbsp olive oil, tahini, dill, water, capers, honey, 1/2 tsp salt, and 1/4 tsp black pepper to a large bowl.

Squeeze the charred lemon into the dressing mixture and blend until smooth.

Combine the toasted panko breadcrumbs, Parmesan cheese, and fresh chives in a clean large bowl.

Add the arugula to the roasted cabbage and toss until lightly wilted.

Transfer the cabbage and arugula to serving plates, then scatter over the Parmesan panko topping.

Drizzle with the charred lemon-dill dressing and toss gently before serving.