Blanch the green beans: Bring a large pot of water to a boil, then drop in green beans. Boil until bright green and crisp-tender, about 2 minutes. Drop the cooked beans into an ice bath to shock the green beans and stop the cooking (for ease, empty then refill the ice bath used for the eggs). Drain and set aside.
Hard boil the eggs: In a small pot, bring just enough water to cover the eggs to a gentle boil. Reduce the heat to a simmer and gently lower the eggs in with a slotted spoon. Bring water to a low, rumbling boil, then let cook for 9 minutes. A few minutes before the eggs are finished cooking, prepare an ice bath. Remove the eggs from the boiling water and plunge into the cold water. Let rest a few minutes, then tap the eggs with back of a spoon to crack them (this will make peeling easier). Return to the ice water to cool completely, then peel and cut into wedges.