Preheat oven to 400°F. Place lentils in a medium pot, covered by about 2 inches of salted water. Bring to a boil then simmer until tender, but slightly firm, about 20 minutes. Drain water and set aside.
Place root vegetables in a large pot, covered by about 2 inches of salted water. Bring to a gentle boil and continue cooking until vegetables can be easily pierced by a fork, about 20 minutes. Drain and place in a food processor with vegan butter and nutritional yeast. Pulse to blend until smooth. Do this in two batches, if necessary, so that everything can get pureed evenly. Taste and adjust seasonings. Alternatively, use a potato masher, but expect a lumpy texture.
While the lentils and root vegetables are cooking, heat oil in a large pan over medium heat. Add leeks, carrots, celery, and thyme. Sprinkle with salt and pepper. Cook until tender for about 10 minutes. Add garlic and cook for another minute or two. When vegetables are tender, sprinkle cornstarch over vegetables and stir. Add tomato paste, Worcestershire sauce, and broth, then stir to mix. Add the cooked lentils and frozen peas to the pan and stir to combine. If the sauce is too thick, add a little water or broth to thin. Taste and adjust seasonings. Transfer mixture to a lightly oiled, oven-proof baking dish and spread evenly.
Spread the root vegetable puree evenly on top of the lentil filling. Rake it over with a fork or make swirls with a spoon to create peaks that will brown nicely. Place the dish into the preheated oven and cook until browned, about 25 to 30 minutes. Serve immediately.