Preheat an oven to 400 Line a baking sheet with parchment paper.
Sprinkle salmon with salt and pepper. Roast for 10-12 minutes until salmon is medium rare.
Meanwhile, cook green beans in boiling water for about 1 minute. They should be cooked but still crispy. Drain and plunge in an ice bath to stop the cooking.
To prepare the dressing, mix anchovies, salt, pepper, and dijon together to form a paste. Then add lemon juice and olive oil. Whisk to emulsify all ingredients together.
In two large bowls (or mason jars), assemble the salad starting from the bottom: lettuce, green beans, salmon, olives, capers, and hard boiled eggs. Keep dressing separate and pour over right before serving.