Rinse the lentils under cold water. In a large pot, combine lentils with vegetable broth, bring to a boil, and then reduce to a simmer until tender, about 20 minutes. In a separate pan, heat olive oil and sauté onion, garlic, carrots, and celery until softened. Add tomato paste and cook for another minute before stirring in the cooked lentils, peas, salt, pepper, and nutmeg. Let simmer until thickened.

While the filling is cooking, peel and cube the potatoes. Boil in salted water until fork-tender. Drain and mash with milk, butter, and salt until smooth and creamy.

Preheat oven to 375°F. Spread the lentil mixture evenly in a 9x13-inch baking dish. Layer the mashed potatoes on top, smoothing with a spatula. Bake for 30 minutes until the top is golden brown. Let cool slightly before serving.

Slice the shepherd's pie into servings and plate. It's great on its own or accompanied by a green salad or crusty bread.

Allow leftovers to cool completely. Store in an airtight container in the refrigerator for up to 4 days. Reheat slices in the oven or microwave before serving.