Pulse nuts in a food processor until finely ground.

Rinse trout and pat dry. Using a sharp knife, slowly remove the skin from the fish. Then, divide the fish into 4 separate portions. Season with salt and pepper.

Beat eggs in a pie plate. Spread ground nuts on a dinner plate. Dip both sides of trout first in egg and then nuts. Heat oil in a 12-inch heavy skillet over moderate heat until hot but not smoking and cook trout, shaking skillet to prevent sticking and turning once with a metal spatula, until browned on both sides and just cooked through, about 12 minutes total.

While trout is cooking, toss arugula in olive oil and lemon juice. Season with salt and pepper, then divide the greens onto 4 plates. Sprinkle each plate with a few dried cherries.