Preheat oven to 375˚. Place one oven rack in the middle and one in the upper third of the oven.

In a small saucepan over medium heat, add the butter and let it cook until it begins to foam and brown bits start to form at the bottom of the pan, about 6 minutes. Add 3 tablespoons of brown butter to a small bowl and set aside.

Place the cut cabbage, carrots, and onions into a large mixing bowl and set aside.

In a medium-sized bowl or 4-cup measuring pitcher, add the grated garlic, half and half, dijon, nutmeg, thyme, parsley salt, and pepper. Whisk until combined. Gently whisk in the remaining brown butter. Pour over the bowl of vegetables and gently toss. Place vegetables in an even layer on a large baking sheet. Sprinkle the shredded Gouda in an even layer over the vegetables. Place the sheet pan on the middle rack of the oven and bake for 15 minutes.

While the vegetables are baking, prepare the topping.

Add the panko, parmesan, parsley, salt, and pepper to the small bowl of brown butter. Mix until well combined.

After 15 minutes, remove the vegetables from the oven and gently mix, moving the vegetables around on the sheet pan. Add the panko topping in an even layer and return the vegetables to the middle rack of the oven; bake for an additional 15 minutes.

After the vegetables have become fork-tender, set the oven broiler to high, and place the sheet pan of vegetables on the upper third oven rack. Let the vegetables sit under the broiler for about 2-3 minutes, moving the sheet pan around so the panko doesn't burn. Remove the vegetables from the oven when the panko is toasted and bits of vegetables are lightly charred. Remove from oven and let cool for five minutes before serving.‍