Pat fish dry and season with salt, pepper and oregano. Drizzle with oil.
Heat a cast-iron skillet, grill pan or griddle pan over medium-high heat.
In another deep-sided skillet, bring a couple of inches of water to a boil. Add salt and par-boil the beans for 3 minutes; cold-shock and dry.
In a large skillet, heat olive oil, 4 turns of the pan, and melt the anchovies into the oil until completely melted. Add green beans and lightly brown; add garlic, chili, tomatoes, olives and capers, cover and cook to slump tomatoes, 6-8 minutes, shaking frequently. Wilt in herbs and remove pan from heat.
Grill or griddle fish for 3-4 minutes on each side and caramelize the halved lemon, cooking it cut-side down; douse fish with its juice.
Serve fish on platters topped with a mound of Puttanesca-style green beans.