How to Make It
Preheat the oven to 350°. Pierce the potatoes all over with a fork and wrap each one in foil. Put the beets and potatoes in a small baking pan, add 1/2 cup of water and cover the pan with foil. Bake for about 45 minutes, until the potatoes begin to soften. Unwrap the potatoes and let cool. Continue baking the beets for about 45 minutes longer, until just tender; let cool.
Meanwhile, in a small saucepan, cover the quinoa with 1/2 cup of water. Bring to a boil, then cover and cook over low heat until the water is absorbed and the quinoa is tender, about 10 minutes. Let cool to room temperature.
Peel the potatoes and coarsely shred them on a box grater. In a large bowl, combine the red onion, capers, parsley, mustard and lemon zest. Add the grated potatoes and the quinoa and mix well. Season with salt and stir in the egg white. Shape the mixture into 12 cakes. Arrange the cakes on a baking sheet and refrigerate for 30 minutes.
Peel the beets and cut them into 1/4-inch dice. In a bowl, toss the beets with the wine vinegar and olive oil and season with salt.
Combine all of the ingredients except the salt in a bowl. Season the sauce with salt.
Preheat the oven to 325°. In a large nonstick skillet, heat 1/4 inch of vegetable oil. Lightly dust the potato cakes with flour and add half of them to the skillet. Cook over moderately high heat for 1 minute. Lower the heat to moderate and cook until browned on the bottom, about 2 minutes. Turn the cakes and cook until browned on the other side, about 3 minutes. Transfer the cakes to a rimmed baking sheet and keep warm in the oven while you fry the remaining cakes; add more oil to the skillet if necessary.
Transfer the potato cakes to plates. Top with the smoked salmon and spoon the beet salad and cornichon sauce alongside. Garnish with the chopped eggs, parsley leaves and dill sprigs and serve.