Preheat your oven to 375°F (190°C).
Prepare the filling: Heat the olive oil in a large oven-safe skillet or Dutch oven over medium heat. Add the chopped onion, carrots, and celery. Sauté until softened, about 8-10 minutes.
Add the minced garlic and cook for another minute until fragrant.
Stir in the rinsed lentils, vegetable broth, tomato paste, thyme, rosemary, and smoked paprika. Bring to a boil, then reduce heat, cover, and simmer for 30-40 minutes, or until the lentils are tender and most of the liquid has been absorbed. Stir occasionally.
While the lentils are simmering, prepare the topping: Place the peeled and quartered potatoes in a large pot and cover with cold water. Add a pinch of salt. Bring to a boil and cook for 15-20 minutes, or until fork-tender.
Drain the potatoes well and return them to the pot. Add the plant-based milk, vegan butter, salt, white pepper, and nutmeg (if using). Mash until smooth and creamy. Be careful not to overmix.
Once the lentil filling is cooked, stir in the frozen peas and season with salt and pepper to taste. If the filling seems too liquidy, simmer uncovered for a few more minutes to thicken.
Spread the lentil filling evenly in the bottom of your oven-safe skillet (or transfer to a 9x13 inch baking dish if not using an oven-safe skillet).
Carefully spoon the mashed potato topping over the lentil filling, spreading it evenly to cover the entire surface. You can create decorative swirls with a fork if desired.
Place the skillet or baking dish on a baking sheet (to catch any potential drips) and bake for 25-30 minutes, or until the topping is lightly golden and the filling is bubbling around the edges.