Adjust oven rack to upper-middle position and heat broiler. Toss potatoes with 2 tablespoons of the butter, 1 teaspoon salt, and ¼ teaspoon pepper in large bowl. Wrap tightly with plastic and microwave until potatoes are tender, about 7 minutes.
While potatoes are cooking, cook beef and onion in large heatproof skillet over medium-high heat until beef is no longer pink, about 5 minutes. Drain beef mixture in colander.
Return drained beef mixture to pan. Stir in thyme and flour and cook until incorporated, about 1 minute. Stir in broth, tomato paste, and Worcestershire. Cook until sauce is thickened, about 5 minutes. Stir in pea and carrot medley and simmer until heated through, about 1 minute. Season with salt and pepper.
Scatter cooked potatoes over beef mixture and brush with remaining butter. Broil until potatoes are golden brown, 3 to 5 minutes. Serve.