Combine almond meal, flour, lemon zest, Kosher salt, and black pepper in a mixing bowl, then whisk well. Place eggs in a shallow bowl, then whisk.
Pat fish filets dry on all sides with a paper towel, then place in the bowl with the egg and coat on all sides. Allow excess egg to drip off, then place in the almond mixture. Cover completely, then press firmly to make sure it’s evenly coated on all sides.
In a large nonstick skillet, heat neutral oil and butter over medium-high heat. When the butter has melted, add fish fillets to the pan and cook. Using a fish spatula, carefully flip the fish over and cook. Transfer to a serving plate.
Squeeze the juice of half of a lemon into the remaining butter, then stir until well mixed. Taste, adjust seasoning, and then stir in. Pour or spoon the sauce on top of the sole, then garnish with additional fresh parsley or chives.