Fish: Wash the salmon fillets and pat dry with paper towels. Turn the fish skin side up. Drizzle with olive oil and season with salt and black pepper (go light with the salt). Heat up a frying pan over high heat and drizzle in some olive oil. Place the fillets skin side down and reduce the heat down to medium. Without touching the fish, let it pan-fry until the skin is crispy golden, about 3-5 minutes. Turn the fish and pan-fry until cooked through, another 2-3 minutes. Transfer the fillets onto a plate and keep warm.
Sauce: Discard the oil in the frying pan and turn the heat down to low. Melt the butter and when the foam has subsided, add in the garlic and lemon zest and sauté until fragrant. Add in the lemon juice and capers and sauté for a minute. Stir in parsley and keep warm.
Sautéed French Beans: Bring a pot of water to boil. Blanch the French beans in hot water for 30 seconds to 1 minute. Drain and set aside. In a frying pan, melt the butter over low heat and when the foam has subsided, sauté the French beans and until they are coated with the butter. Season with salt and pepper to taste.
Serve: Scoop a mound of potato-carrot mash on the plate. Place the salmon fillet on top of the mash and scoop the sauce on top of the fillet. Place the sautéed French beans on the side and serve.