Preheat and Prep:

1. Preheat your oven to 375°F (190°C).
2. Grease a 9×13-inch baking dish lightly with cooking spray or butter.

Cook the Ground Beef Mixture:

1. In a large skillet or Dutch oven over medium-high heat, add the ground beef.
2. Once the beef begins to brown, add the diced onion, minced garlic, and green bell pepper (if using).
3. Cook for about 5–7 minutes until the beef is fully browned and the vegetables have softened.
4. Season with salt, black pepper, smoked paprika, and dried thyme. Stir well and remove from heat.

Prepare the Potatoes:

1. In a large bowl, toss the cubed potatoes with a little salt and pepper.
2. (Optional: For extra flavor, you can roast the potatoes in the oven for 10 minutes before assembling.)

Make the Cheese Sauce:

1. In a small saucepan over medium heat, whisk together the milk and flour until smooth.
2. Bring the mixture to a simmer, stirring continuously until it thickens slightly (about 3–4 minutes).
3. Remove from heat and stir in 1/2 cup of the shredded cheddar cheese until melted. Adjust seasoning with salt and pepper as needed.

Assemble the Casserole:

1. In your prepared 9×13-inch dish, evenly spread the browned ground beef mixture.
2. Layer the cubed potatoes and thawed peas and carrots evenly over the beef.
3. Pour the cheese sauce over the top, then sprinkle the remaining 1 1/2 cups of shredded cheese evenly over the casserole.

Bake:

1. Cover the dish with aluminum foil (optional) and bake in the preheated oven for 35–40 minutes, or until the potatoes are tender and the cheese is bubbly and golden.
2. Remove the foil in the last 5–10 minutes of baking for a crispier cheese topping if desired.

Garnish and Serve:

1. Remove the casserole from the oven and let it rest for 5 minutes before serving.
2. Garnish with chopped fresh parsley and serve hot.