In a saucepan combine the water, sugar and honey. Bring to a simmer over medium heat and stir until the sugar and honey dissolves. Sometimes the honey will create a white foam on top of the syrup. You can use a small ladle to skim the foam off the top to create a clear syrup.
Add the dried chamomile flowers to the syrup and simmer on low for a couple of minutes. Turn off the heat and let steep for 15 to 20 minutes. Strain the syrup through a fine mesh strainer. Cool the syrup before using. Store in the refrigerator. This recipe will make approximately 2 cups of syrup and will keep for several weeks in the fridge.
To make the cocktail
Add ice to a cocktail shaker and then add the gin, chamomile honey syrup, fresh lemon juice, 2 dashes of grapefruit bitters and the egg white. Shake vigourously for 15 to 20 seconds to fully mix in the egg white. Strain into a coupe glass and enjoy!