Cook's Note: Orange flower water is available at better liquor stores and Middle Eastern markets. Be very careful when adding this to your cocktail as it can easily overwhelm the flavors in this delicious drink.
Add the gin, half-and-half, simple syrup, orange flower water, vanilla if using, egg white and lemon and lime juices in a cocktail shaker. Shake vigorously for 3 minutes, or blend with an immersion blender until frothy, about 20 seconds. Pour into an ice-filled highball glass, and top with the seltzer water.
Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the risk of Salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell. For recipes that call for eggs that are raw or undercooked when the dish is served use shell eggs that have been treated to destroy Salmonella, by pasteurization or another approved method.