Step 1

Halve the cabbage and cut into 1-inch chunks. Set aside.

Step 2

Place an broiler-safe pan or skillet paired with a tight-fitting lid over medium heat. Add in the butter, garlic and cabbage. Season with salt and pepper, and cook, stirring occasionally, until the cabbage is lightly golden around the edges and softened, 3 to 5 minutes.

Step 3

Add in the red pepper flakes and broth and bring to a boil. Cover the pan, turn the heat down to low, and allow the cabbage to braise until the cabbage is tender, 20 to 25 minutes.

Step 4

Meanwhile, prepare the topping by combining the butter, garlic and parsley in a medium bowl. Season with salt and pepper and stir well to combine then spread the garlic butter over the bread. Beat together the egg and milk in the same bowl. Roughly cut or tear the garlic buttered bread into small pieces and add to the egg mixture along with the Parmigiano-Reggiano. Stir well to combine.

Step 5

When the cabbage is tender, remove the lid and top with the bread mixture. Place the pan on the center rack of your oven and turn the broiler to high. Broil until the top is well browned and set, 5 to 7 minutes.