Use a paring knife to cut four slits into both sides of each snapper, cutting through the skin and flesh. Whisk half of the lemon juice in a bowl with the oregano and half of the olive oil. Salt each fish liberally and put in a nonreactive container. Put the fish in a dish and pour the lemon mixture over them. Let sit at room temperature for 1 hour, turning the fish after 30 minutes to take in the marinade.
Lay out five grape leaves on the counter, making sure to overlap them to create a sheet that is as wide as the fish is long, and long enough to wrap around the snapper 1 1/2 times. Wrap one of the fish in the leaves. Repeat with the remaining grape leaves and snapper. Brush with the remaining olive oil and set aside.
Heat a grill to medium-high. In a 2-quart saucepan, combine the stock, garlic, and remaining lemon juice. Bring to a simmer. Remove from the heat and whisk in the egg. Return the pan to the stovetop over low heat and, stirring constantly, cook until the sauce thickens (make sure it does not get too hot or the eggs will scramble). Set it in a warm spot on the stove.
Grill the fish for 4 minutes per side, making sure not to burn the grape leaves.
To serve, set one whole wrapped fish on a serving plate and top with the sauce.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.