Remove skin from grapefruit and cut fruit into quarters. Place all four pieces into a shaker with a sprig of fresh thyme, and muddle it to extract all the juice from the grapefruit and the essence of the thyme.
Add whisky, grappa, maple syrup and pear nectar. Add bitters and egg white, if using. Fill shaker with ice and shake vigorously.
Strain and pour into a champagne saucer or other wide-mouthed glass. Garnish with thyme. Serve straight up.