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.