Prepare the Oven: Set your oven to 375°F (190°C) to preheat.
Cook the Chicken : Heat 2 tablespoons of butter in a large skillet over medium heat. Add the chicken pieces and sauté for 5–7 minutes, or until golden brown and fully cooked. Remove the chicken from the skillet and set it aside.
Sauté the Vegetables: In the same skillet, add the remaining butter. Cook the onions and mushrooms, stirring occasionally, until they become tender and lightly browned, about 4–5 minutes. Remove from heat.
Prepare the Creamy Sauce: In a medium bowl, whisk together the chicken broth, heavy cream, salt, pepper, thyme, mayonnaise, Dijon mustard, and lemon juice.
Combine with Cheese: Stir in 1¼ cups of the shredded Gouda or Swiss cheese and ¼ cup Parmesan cheese into the sauce mixture until smooth.
Layer the Ingredients: In a 9x13-inch baking dish, arrange the steamed asparagus and sautéed mushrooms and onions. Top with the cooked chicken pieces.
Add the Sauce: Pour the creamy cheese sauce evenly over the chicken and vegetables. Gently stir to ensure everything is well-coated.
Top with Cheese: Sprinkle the reserved ¼ cup Gouda or Swiss cheese and ¼ cup Parmesan cheese evenly on top.
Bake: Bake in the preheated oven for 20–25 minutes, or until bubbly and golden on top.
Serve Hot: Let the bake cool for a few minutes before serving. Pair with rice, mashed potatoes, or crusty bread for a complete meal.