Preheat the oven to 425°F (220°C). Lightly oil the sheet pan.

Mix melted unsalted butter, olive oil, fresh thyme, minced garlic, salt, and black pepper in the small bowl.

Cut the green cabbage into 3/4-inch-thick rounds. Arrange the rounds in a single layer on the oiled sheet pan.

Divide the garlic-herb butter mixture over the cabbage rounds. Brush the tops and sides until coated.

Roast the cabbage for 40 to 50 minutes. Cook until tender and deeply browned at the edges.

Broil the cabbage for 1 to 2 minutes. Watch closely until the tops are charred and crisp.

Chop the pistachios and Parmesan cheese together on the cutting board. Add arugula and continue chopping into a coarse crumble.

Add lemon zest, salt, and black pepper to the crumble. Mix until evenly combined.

Transfer the roasted cabbage rounds to serving plates. Spoon the lemon-pistachio-Parmesan crumble over each portion.

Drizzle with tahini and honey if desired. Serve immediately while the cabbage is hot.

Drizzle with tahini and honey, if using.