How to Make It
In a large skillet, melt 1 tablespoon of the butter. Add the shallot and garlic and cook over moderately high heat, stirring, until softened, about 1 minute. Add the almond milk and cream and simmer until slightly thickened and reduced by half, about 4 minutes. Add the spinach and cook, stirring, until wilted, about 3 minutes; season with salt and pepper. Transfer the spinach to a bowl and keep warm.
Wipe out the skillet and heat 1 tablespoon of the oil. Season the trout with salt and pepper. Add 2 of the trout fillets to the skillet, skin side down, and cook over moderately high heat until the skin is crisp and golden brown, about 5 minutes. Flip the fillets and cook until the fish is just cooked throughout, about 4 minutes. Transfer to a platter and keep warm. Repeat with the remaining olive oil and trout fillets.
Add the remaining 4 tablespoons of butter to the skillet and cook until it just begins to brown, 3 to 4 minutes. Add the almonds and toast them, stirring, until golden brown, about 2 minutes. Stir in the parsley and lemon juice and spoon the sauce over the fish. Top with the arugula and serve at once, with the spinach.