Preheat your oven to 375°F (190°C).

In a microwave-safe dish, add your asparagus with ¼ cup of water. Cover it tightly and steam in the microwave for about 3 minutes, or until it's bright green and slightly tender. Drain the water and set the asparagus aside.

In a large skillet, melt a generous tablespoon of butter over medium-high heat. Add the chicken pieces and cook for about 6 minutes, or until browned and cooked through. Transfer it to a greased casserole dish and top with the asparagus.

In the same skillet, add chopped onion and sliced mushrooms. Sauté for about 4-5 minutes until tender and fragrant.

Pour in chicken broth and heavy cream, then sprinkle in the salt, pepper, thyme, mayonnaise, mustard, and lemon juice. Simmer for about 8-10 minutes until the mixture thickens.

Stir in your choice of gouda or swiss cheese until melted and incorporated into the sauce.

Pour the creamy sauce over the chicken and asparagus. Ensure each piece is well coated.

Bake in the preheated oven for about 30 minutes until bubbling and the chicken reaches an internal temperature of 165°F (74°C).

Let the casserole sit for a few minutes before serving, garnished with parsley or chives.