Boil the sweet potatoes in salted water until soft, about 15 minutes. Drain and set aside.
Mash them with olive oil, non-dairy milk, salt, and black pepper. Set aside.
Heat olive oil in a skillet over medium heat. Sauté onion and garlic until fragrant.
Add mushrooms and cook until softened, about 5 minutes.
Stir in lentils, peas, carrots, tomato paste, broth, thyme, paprika, salt, and black pepper. Let it simmer for 5 minutes.
Transfer the filling to a baking dish and spread evenly.
Top with the mashed sweet potatoes and smooth out the surface.
Bake at 375°F (190°C) for 15 minutes or until slightly golden.
Let it cool for a few minutes before serving.