Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish.
In a large saucepan, combine the wild rice blend and chicken broth. Bring to a boil, then reduce heat and simmer for about 45 minutes or until the rice is tender. Drain any excess liquid.
While the rice cooks, season the chicken with salt and pepper. In a large skillet, cook the chicken over medium heat until no longer pink in the center, about 6-8 minutes per side. Remove from the pan and cut into bite-sized pieces.
In the same skillet, melt 2 tablespoons of butter. Add onions, celery, carrots, and mushrooms. Sauté until vegetables are softened, about 5-7 minutes. Add minced garlic and cook for another minute.
Time for the creamy sauce! In a separate saucepan, melt the remaining butter. Whisk in the flour and cook for 1-2 minutes. Gradually add milk and cream, whisking constantly to prevent lumps. Add thyme, rosemary, salt, and pepper. Simmer until the sauce thickens.
In a large bowl, combine the cooked wild rice, chicken, sautéed vegetables, creamy sauce, and frozen peas. Mix well.
Transfer the mixture to your prepared baking dish. Sprinkle Parmesan cheese on top.
Bake for 25-30 minutes, until the casserole is bubbly and the top is golden brown.