Begin by heating a large pot or Dutch oven over medium-high heat. Add the ground beef (or turkey) and cook, breaking it up with a spoon, until it is browned and fully cooked. This should take about 5-7 minutes. If there’s excess grease, carefully drain it off to avoid an overly oily soup. The browned meat will provide a deep, savory base for the soup.
Once the meat is browned, add the chopped onion and diced carrots to the pot. Stir everything together and cook for about 3-4 minutes, or until the onion becomes soft and translucent. Next, add the minced garlic and cook for another minute, stirring constantly to prevent burning. The vegetables will release their natural sweetness, enhancing the flavor of the soup.
Pour in the beef broth, stirring well to combine. Add the dried thyme (or rosemary), along with salt and pepper to taste. Bring the soup to a gentle simmer, then reduce the heat and let it cook for about 15-20 minutes. This allows the flavors to meld together and the vegetables to become tender. Stir occasionally to ensure everything cooks evenly.
While the soup is simmering, prepare the mashed potatoes. In a separate pot, bring a large amount of water to a boil and add the peeled, chopped potatoes. Cook for about 12-15 minutes, or until the potatoes are fork-tender. Drain the water and return the potatoes to the pot. Add the butter and milk (or cream), then mash until smooth and creamy. Season with salt to taste. If you prefer extra richness, you can stir in a handful of shredded cheddar cheese.
Once the soup has simmered and the vegetables are tender, add the peas. Since peas cook quickly, they only need about 2-3 minutes in the hot broth. Give the soup a final taste and adjust the seasoning if needed. If the soup seems too thick, you can add a little more broth to reach your desired consistency.
To serve, ladle the hot soup into bowls. Top each bowl with a generous scoop of the creamy mashed potatoes, creating the signature "shepherd’s pie" effect. If using, sprinkle shredded cheddar cheese on top and allow it to melt slightly. For an extra touch, garnish with fresh thyme or a sprinkle of black pepper.