Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with cooking spray or olive oil.
In a large skillet over medium heat, add the olive oil and sauté the diced onion until translucent, about 3-4 minutes. Add the minced garlic and cook for another minute.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and no longer pink, about 5-7 minutes. Drain excess fat if necessary.
In a large bowl, mix together the cream of mushroom soup, milk, salt, black pepper, paprika, and thyme until well combined.
Layer half of the sliced potatoes in the bottom of the prepared baking dish. Spread half of the beef mixture over the potatoes, followed by half of the soup mixture. If using, sprinkle half of the frozen mixed vegetables on top.
Repeat the layers with the remaining potatoes, beef mixture, soup mixture, and vegetables.
Cover the baking dish with aluminum foil and bake in the preheated oven for 45 minutes.
Remove the foil and sprinkle the shredded cheddar cheese evenly over the top. Return to the oven and bake uncovered for an additional 15-20 minutes, or until the cheese is melted and bubbly, and the potatoes are tender.
Let the casserole cool for 5-10 minutes before serving.