Preheat your oven to 400°F (200°C).
In a large skillet over medium heat, brown the ground beef until fully cooked. Drain any excess fat from the pan.
Add the chopped onion, diced carrots, and minced garlic to the skillet. Sauté for 5-7 minutes, or until the vegetables are tender.
Stir in the tomato paste, Worcestershire sauce, beef broth, and dried thyme. Season liberally with salt and pepper.
Allow the mixture to simmer for about 10 minutes to let the flavors meld and the liquid reduce slightly.
Add the frozen peas to the beef mixture and stir to combine. Remove the skillet from the heat.
Spread the beef mixture evenly into the bottom of a baking dish.
Top with the prepared mashed potatoes, spreading them out carefully to cover the beef completely. Use a fork to create texture on the surface.
If desired, sprinkle shredded cheddar cheese on top of the potatoes.
Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and the filling is bubbling around the edges.