First make the shrub. Add the raspberries, thyme, sugar and vinegar to a medium pot. Heat to just a simmer and cook for about 10 min. Do not boil. Let the mixture cool completely. If you have the time, let the thyme and raspberries sit in the sugar and vinegar liquid for as long as you can. Even up to 2 or 3 days, but you can also use it right away. Strain the shrub and store in an airtight container in the fridge.
To make the cocktail, add the gin, liqueur, lemon, shrub and egg white to a cocktail shaker. Give it a good shake and pour into a short glass. Top with club soda and serve!