Beat the eggs in a mixing bowl until thick and light in colour. Combine the eggs with the matzo meal, vegetable oil, 1 tablespoon chicken stock, vodka, salt, pepper, basil and soda water in a large bowl. Stir until well blended. Cover and refrigerate 1 to 2 hours.
Pour the remaining chicken stock into a large saucepan and bring to the boil over medium high heat.
Meanwhile, form walnut-sized balls using the chilled matzo mixture. Place the balls in the chicken stock, reduce heat to medium and simmer until matzo balls are cooked through, 45 to 60 minutes.