- Make salsa verde by combining chopped anchovies, capers, herbs, garlic, and shallot. Mix well. Combine with olive oil, black pepper, red pepper flakes, and cumin. Salt to taste.
- To prepare fish, clean, scale, gut, and wash snapper (or have fishmonger do this for you). Pat dry. Stuff stomach cavity with thyme and lemon.
- Heat grill and rub snapper all over with salt and pepper. Grill 8 to 10 minutes on each side.
- Toss potatoes with olive oil, salt and pepper and add to grill until crispy and golden brown.
- In mixing bowl, toss red potatoes, 1⁄4 of prepared salsa verde, and arugula. Cover snapper with remaining salsa verde, top with potatoes and arugula, and serve.