Preheat broiler to high. Arrange figs, cut-side up, on the broiler rack. Brush with 2 tablespoons honey. Sprinkle chopped rosemary over, if using.
Place under pre-heated broiler for 5-6 minutes, or until just beginning to caramelize.
To make the sabayon, lightly whisk the eggs with the remaining honey in a large, heatproof bowl, then set over a saucepan of simmering water. Using a handheld electric mixer, beat the eggs and honey together for about 10 minutes, or until pale and thick.
To plate, place 4 fig halves on 4 serving plates, add a generous spoonful of the sabayon, and serve immediately.