Preheat the oven to 375°F (190°C).
In a large skillet, melt the butter over medium heat.
Add the diced onion and sliced mushrooms to the skillet and sauté for 5 minutes until softened.
Add the minced garlic and cook for 1 more minute until fragrant.
Sprinkle the flour over the vegetables and stir well to coat; cook for 2 minutes to remove the raw flour taste.
Gradually whisk in the chicken broth and milk, stirring constantly until the mixture thickens and becomes smooth, about 3-5 minutes.
Stir in the dried thyme, dried sage, salt, and black pepper.
Add the shredded turkey and thawed mixed vegetables to the sauce, stirring to combine evenly.
Transfer the turkey and vegetable mixture into a 9×13-inch casserole dish and spread evenly.
Spread the cooked mashed potatoes evenly over the turkey mixture.
Sprinkle the shredded cheddar cheese evenly over the mashed potatoes.
In a small bowl, mix the crushed buttery crackers with the chopped fresh parsley.
Sprinkle the cracker and parsley mixture evenly over the cheese layer.
Bake uncovered in the preheated oven for 30-35 minutes, or until the topping is golden brown and the casserole is bubbly.
Remove from the oven and let rest for 5 minutes before serving.