Combine the beef, carrots, onion, broth, beer, Worcestershire, tomato paste, flour, 1½ teaspoons salt, and 1 teaspoon pepper in a 4- to 6-quart slow cooker. Nestle the potatoes in the liquid.
Cover and cook until the potatoes are tender, on low for 7 to 8 hours or on high for 4 to 5 hours. Transfer the potatoes to a medium bowl. Stir the peas into the stew, cover, and warm until heated through, 2 to 3 minutes.
Mash the potatoes with the milk, butter, and ½ teaspoon each salt and pepper in a medium bowl.
Serve the stew topped with the mashed potatoes.