Place 2/3 of the diced potatoes in a pot, cover with salted water by 1 inch, bring to a boil, and cook for 15–20 minutes until fork-tender. Drain and mash with butter and sour cream. Set aside.

In a large pot over medium-high heat, cook ground beef, onion, and carrots until beef is no longer pink and vegetables soften, about 6–8 minutes.

Add garlic and tomato paste, cooking for 1 minute. Stir in beef broth, remaining diced potatoes, Worcestershire sauce, rosemary, thyme, and bay leaves. Bring to a boil, reduce to a simmer, and cook for 15 minutes until potatoes are tender.

Stir in mashed potato mixture until soup thickens slightly and is well combined.

Add heavy cream and grated cheddar cheese in batches, stirring until melted and smooth.

Stir in frozen peas and cook for 2 minutes until heated through. Discard bay leaves and season to taste.