In a large skillet, brown the ground beef over medium heat, breaking it up into crumbles as it cooks. Once the beef is no longer pink, remove it from the skillet and set it aside.
1. In the same skillet, add the chopped onion and minced garlic. Sauté them until they become fragrant and the onion turns translucent. Next, add the diced carrots and celery to the skillet. Cook for a few minutes until the vegetables begin to soften.
Return the cooked ground beef to the skillet and mix it with the vegetables. In a separate bowl, whisk together the condensed cream of mushroom soup, milk, dried thyme, salt, and pepper until well combined. Pour this mixture over the ground beef and vegetables, stirring gently to evenly distribute the sauce.
Add the frozen peas to the skillet and stir them into the mixture. Allow the casserole to simmer for about 5 minutes, allowing the flavors to meld together. Transfer the beef and vegetable mixture to a greased 9x13-inch (23x33cm) baking dish.
Spread the cooked mashed potatoes evenly over the top of the beef mixture. You can use a spatula to create a decorative pattern if desired. Place the casserole in the preheated oven and bake for 30 minutes, or until the potatoes turn golden brown and the casserole is heated through.