Crack your egg into a bowl, add the lemon juice and corn starch and whisk. While whisking slowly pour the stock into the egg/lemon mix then transfer to a pot.
Add the wine, turn the heat to medium and stir for 2-3 minutes or until thickened. Adjust with salt and pepper (add more stock if too lemony, add more lemon juice if desired). Take off the heat.
Ensure your salmon has come to room temperature. Pat-dry with paper towel and season both sides with salt and pepper.
Place a large non-stick pan on your stovetop over medium-high heat. Add olive oil and place fillets in the pan. Saute for 2-3 minutes or until you see the sides of the fish turn opaque to almost the middle of the fish (look sideways at the fish).
Flip the fish, cook for another 2 minutes, remove pan from the heat.
Place green beans on your plate and place salmon on the plate. Spoon over Avgolemono sauce and garnish with chives and and some dill.
A side of rice pilaf goes splendidly with this dish.