Preheat oven to 420 degrees. 

Place the potatoes in a large pot, cover with cold water, add about 3 tablespoons of salt. Place over high heat, bring to a boil and reduce heat to medium low, cooking the potatoes at a gentle simmer. Cook until fork tender, about 30 to 40 minutes. Drain potatoes from the water and set aside to cool. 

Grease an 11 x 5 inch casserole dish with 1 teaspoon of olive oil. Set aside. 

Heat 4 tablespoons of olive oil in a saucepan over medium high heat. Once oil is hot, add the onions and sugar and saute until golden brown, about 15 minutes. Set aside. 

Separate the egg yolks and egg whites. Reserve egg yolks. Place the egg whites into a stand mixer with a whisk attachment and beat on low for about 2 to 3 minutes. Increase speed to medium and whip the eggs for another 3 to 5 minutes until stiff peaks have formed. Set aside. 

Peel the potatoes and discard the skins. Smash the potatoes with a fork until a puree like consistency is formed. 

Place the smashed potatoes into a large mixing bowl. Add the caramelized onions, salt, pepper, cumin, nutmeg and egg yolks. Mix all the components with a large fork until combined well. Pour the whipped egg whites into the potato mix and gently fold it in until combined. Gently transfer the mixture into the casserole dish. Smooth out the top layer with a spatula. Sprinkly 1 teaspoon of olive oil on top and transfer to the oven. Bake for about 40 minutes until the cojada is golden brown on all edges.

Serve hot.