Whisk the egg white in a bowl until it turns very foamy and opaque. Add the rosemary, blood orange juice, lemon juice, and sugar to a cocktail shaker and muddle to release their fragrance. Add crushed ice to the shaker along with the egg white and the rest of the ingredients; cover and shake vigorously for up to 1 minute. Strain into a cocktail glass and garnish with a large rosemary sprig. Enjoy!