Preheat oven to 200°C/400°F. Line a large roasting pan with baking paper.
Place potato and garlic in lined pan; drizzle with 1 tablespoon of the oil and season. Roast for 20 minutes.
Meanwhile, cook beans in a saucepan of boiling water for 2 minutes; remove using a slotted spoon and refresh under cold water. Reserve until required.
Bring water in pan back to the boil. Break one egg into a cup, then slide into pan; repeat with remaining eggs. When all eggs are in the pan, return water to the boil. Cover pan, then turn off heat; stand for 4 minutes or until a light film of egg white sets over yolks. Remove one egg at a time using a slotted spoon; place on paper towel to drain.
Add tomatoes and olives to roasting pan; drizzle with remaining oil. Stir to mix well; roast for 10 minutes.
Push tomato mixture to one side of pan; add seasoned salmon to other side, skin-side down, making sure salmon sits directly on pan. Roast salmon for 2 minutes; turn and roast for a further 2 minutes or until cooked to your liking.
Add green beans and eggs to pan; season to taste. Drizzle with salsa verde. Serve with remaining salsa verde to the side.
Use ocean trout fillets instead of salmon, if preferred.