Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish and set aside.

In a large pot of lightly salted boiling water, add the diced potatoes, sliced carrots, and sliced parsnips. Cook for 5-7 minutes, or until just tender-crisp. Drain well and set aside.

While the root vegetables are par-cooking, heat 1 tablespoon of olive oil in a large skillet or Dutch oven over medium heat. Add the sliced leeks and halved Brussels sprouts. Sauté for 5-7 minutes, until the leeks are softened and the Brussels sprouts are slightly tender. Season with 1/2 tsp salt and 1/4 tsp black pepper. Remove from heat and set aside.

In the same skillet or Dutch oven (no need to clean), melt 4 tablespoons of unsalted butter over medium heat. Whisk in the all-purpose flour and cook for 1-2 minutes, stirring constantly, to create a roux. It should be light golden in color.

Gradually whisk in the warmed whole milk, then the vegetable broth, ensuring no lumps form. Continue to whisk and cook for 5-7 minutes, until the sauce thickens and coats the back of a spoon. Reduce heat to low.

Stir in the shredded Gruyere cheese until melted and smooth. Add the ground nutmeg, dried thyme, and season generously with salt and black pepper to taste. Remove from heat.

In a large mixing bowl, gently combine the par-cooked root vegetables and the sautéed leeks and Brussels sprouts. Pour the creamy cheese sauce over the vegetables and stir gently until everything is well coated.

Transfer the vegetable mixture into the prepared 9x13 inch baking dish, spreading it evenly.

In a small bowl, combine the panko breadcrumbs, grated Parmesan cheese, and 2 tablespoons of melted butter. Sprinkle this mixture evenly over the top of the casserole.

Bake for 35-45 minutes, or until the casserole is bubbly around the edges and the topping is golden brown and crispy.

Remove from the oven and let rest for 5-10 minutes before serving. This allows the sauce to set slightly and prevents it from being too runny.