Preheat your oven to 400°F (200°C). Lightly grease a 9x13 inch casserole dish.

Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Add the chopped onion and cook until softened, about 5-6 minutes. Add the minced garlic and cook for another minute until fragrant.

Add the ground beef to the skillet. Break it up with a spoon and cook until browned all over, about 8-10 minutes. Drain off any excess grease.

Sprinkle the all-purpose flour over the cooked beef and stir well to combine. Cook for 1-2 minutes to toast the flour.

Gradually whisk in the beef broth, ensuring there are no lumps. Stir in the tomato paste, Worcestershire sauce, and dried thyme. Bring the mixture to a simmer and cook for 3-5 minutes, stirring occasionally, until the gravy has thickened.

Remove the skillet from the heat. Stir in the frozen peas and carrots. Season the beef filling with 1 tsp of salt and 1/2 tsp of black pepper, or to your taste. Pour the filling into the prepared casserole dish and spread it into an even layer.

In a large bowl, combine the thinly sliced potatoes, melted butter, 1/2 tsp salt, and 1/4 tsp pepper. Toss gently to coat all the potato slices evenly.

Arrange the seasoned potato slices in an overlapping pattern on top of the beef filling, covering it completely.

Cover the casserole dish tightly with aluminum foil. Bake in the preheated oven for 45 minutes.

Carefully remove the foil. Sprinkle the shredded cheddar cheese evenly over the potatoes. Return the casserole to the oven, uncovered, and bake for another 20-25 minutes, or until the potatoes are tender when pierced with a fork and the cheese is melted, bubbly, and golden brown on top.

Remove the casserole from the oven and let it rest for 10-15 minutes before serving. This allows the filling to set slightly. Garnish with fresh chopped parsley before serving.