How to Make It
In a large saucepan, cover the potatoes with cold water and bring to a boil. Cook over moderate heat until the outsides are tender but the centers are still hard, about 15 minutes. Drain and cool under running water. Peel the potatoes and coarsely grate them. Season with salt and pepper and toss to combine.
Season the trout with salt and pepper. On a cast-iron griddle or skillet, melt 1/2 tablespoon of the butter in 1/2 tablespoon of the oil. Spoon a scant 1/2 cup of shredded potatoes onto the griddle and flatten it into a 5-inch round. Set a piece of trout in the center, cover with a spinach leaf and top with a scant 1/2 cup of potatoes, flattening them. Cook the potato cake over moderately low heat until crispy and golden on the bottom, 5 to 7 minutes. Carefully turn the cake and cook until the potatoes are crisp and golden and the trout is cooked through, about 5 minutes longer; add more butter and oil if necessary. Transfer to paper towels to drain, then serve hot. Repeat with the remaining grated potatoes, trout and spinach, serving the potato-trout cakes hot.