Cook potatoes until tender 15-20 minutes
Cook and drain hamburger. Add 1/4 cup water to the skillet, scraping up browned bits with a wooden spoon. Reduce heat to medium; add onion and carrots. Cook, stirring occasionally, until softened, about 5 minutes. Stir in tomato paste. Add flour; cook, stirring 2 minutes.
Add Worcestershire sauce, 2 cups water and hamburger. Season with 2 teaspoons salt and 1/4 teaspoon pepper. Simmer until thickened, stirring occasionally, about 10 minutes. Stir in peas; cook 1 minute.
In pan, bring milk and butter to a simmer; remove from heat. Return potatoes; mash. Season with 2 teaspoons salt and 1/4 teaspoon pepper. Spread over pie; use a fork to make peaks. Bake on a baking sheet until tops are browned. 25-30 minutes at 425 degrees. Cool slightly