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Step 1
Preheat the oven to 425°F. Spray a 9-inch round cake pan with oil and drizzle 1 Tbsp olive oil at the bottom.
Step 2
Put the potatoes, skin on, in a medium pot and cover with cold water. Bring to boil over high heat, cover, lower the heat and cook until tender, about 25 minutes. Drain and transfer the potatoes to a large bowl. You can either remove potato skins or leave them on for a more rustic results. Mash the potatoes, making sure to leave small to medium chunks.
Step 3
While the potatoes are cooking, put 3 Tbsp olive oil in a pan over medium-high heat and sauté the onion and carrots until carrots are tender, about 8 minutes. Add green pea and sauté about 3 minutes longer (or 1 minute if you’re using frozen peas). Remove from the heat.
Step 4
Add the carrot-pea mixture into the mashed potatoes and mix. Add salt, turmeric, black pepper and egg yolks and mix again.
Step 5
Whip egg whites to form soft peaks and then fold gently into potato mixture. Transfer to the pan and drizzle a little olive oil on top. Bake for 10 minutes, then reduce the heat to 350°F and bake for 30-35 minutes longer, until the top is golden and the pie is firm. Let sit for 10 minutes, then slice and serve.