Boil potatoes in salted water about 15 minutes until tender; drain and mash with 2 tablespoons butter and milk until smooth. Season with salt and pepper; set aside.
Preheat oven to 400°F. Melt remaining 2 tablespoons butter in large skillet over medium-high; cook mushrooms about 8 minutes until deeply browned.
Add onion, carrots, and celery; cook about 6 minutes until softened. Stir in garlic and tomato paste; cook 1 minute until fragrant.
Add lentils, broth, Worcestershire, and thyme; simmer about 10 minutes until liquid halves. Stir in peas; season with salt and pepper.
Transfer filling to 9x13-inch dish; spread potatoes evenly over top, making peaks with fork.
Bake 25-30 minutes until filling bubbles and peaks are golden brown; optionally broil 2-3 minutes for extra crispness. Rest 10 minutes before serving.