Peel the potatoes and cut them in small cubes. Add to a large pot and cover with water. Season the water with salt and place over medium-low heat. Simmer for until 20 minutes or until the potatoes are cooked. Drain. Put the potatoes in your potato ricer and press the potatoes into a bowl or press them through a fine sieve. Add melted butter and heavy cream. Stir to combine using a rubber spatula. The mashed potatoes should be nice and creamy. Season to taste with salt and pepper.
Dice the carrot. Place a pan over medium-high heat. Add olive oil and diced carrots. Cook for 2 - 3 minutes, then add the frozen peas and stir to combine. Add the Alla Luigi Vegan Ragu (if the ragu isn't available in your country, substitute with a canned of crushed tomatoes and 240g (8.5 oz) cooked lentils (feel free to use canned). Pour in the water, stir to combine and bring to a boil. Then, reduce the heat to low and continue to cook for 5 minutes. Season to taste with salt and pepper. Transfer the sauce to an oven-safe dish (20 x 25 cm or 8 x 10 inch).TipYou can use a meat ragu for this sauce as well.
Add egg yolk and grated parmesan cheese to the mashed potatoes. Stir well. Evenly spread the potatoes on top of the veggies. Place the dish with the Vegetarian Shepherd's Pie onto a large baking sheet. Place in the preheated oven, on the middle rack. Bake for 25 - 30 minutes at 200°C / 390°F.
Take the baked Vegetarian Shepherd's Pie from the oven. Let it stand for 10 minutes. Then divide between four plates and serve immediately.