Brown the ground beef in a large skillet over medium heat, breaking it up as it cooks. Add the onion, carrots, and garlic and cook until the vegetables begin to soften.
Transfer the mixture to the slow cooker. Stir in the beef broth, Worcestershire sauce, thyme, salt, and pepper.
Cover and cook on low for 6 hours or until the carrots are tender.
About 30 minutes before serving, place the potatoes in a saucepan and cover with water. Boil until fork-tender, then drain.
Mash the potatoes with the butter and milk until smooth. Season with salt and pepper.
Stir the frozen peas into the beef mixture in the slow cooker. Spoon the mashed potatoes over the top and let everything warm together for 10 minutes on low before serving.