Pre-heat oven to 350 degrees and line a small baking sheet with parchment paper. Arrange halved figs cut side up on the baking sheet. Top each fig with a drop of honey.
Roast figs for 20 minutes, then allow to cool slightly. Add roasted figs and 1/2 oz of lemon juice to a food processor and blend until smooth.
Strain fig puree through a mesh sieve to remove pieces of skin.
Add fig puree, vodka, and remaining lemon juice to a cocktail shaker with ice. Shake vigorously, then divide mixture evenly into two coupe glasses. Top with Elderflower Tonic just before serving.