Preheat oven to 400°F (204°C). Butter a 13x9x3-inch baking dish with 1 tablespoon of the butter or spray with nonstick cooking spray; set aside.

In an 8-quart stockpot, add 1 tablespoon of butter and 1 tablespoon of olive oil. Stir in mushrooms and cook over medium-high heat until golden brown and liquid has evaporated.

Stir in the onion, garlic, and thyme, and cook until onions are translucent, about 6-8 minutes. Stir in wine and cook until it evaporates, about 2 minutes. Transfer the mushroom mixture to a bowl.

Add 3 more tablespoons of the remaining butter to the same stockpot over medium-low heat. Sprinkle flour over melted butter and whisk constantly for 1-2 minutes. Remove from heat and slowly whisk in milk, heavy cream, and broth until smooth.

Stir in nutmeg, salt, and black pepper. Turn up heat to high and bring to a boil. Immediately reduce to a simmer, whisking often, until sauce thickens, about 9-11 minutes.

Cook linguine according to package instructions in well-salted water until al dente. Drain well.

Add cooked chicken and onion mixture and drained linguine to the sauce along with peas and parsley. Mix well until the sauce coats the pasta.

Place the baking dish on a rimmed baking sheet. Pour mixture into prepared baking dish. Top with mozzarella and dot with butter. Bake uncovered for about 25 minutes or until heated through and golden brown on top.

Sprinkle top with parsley to garnish and serve.