Preheat the oven to 180 degrees C
Grease a shallow baking dish with butter and sprinkle with sugar
Shake the sugar around the dish so that it is evenly coated, then tip out any excess
For the batter, heat the butter in a small pan until it turns a pale hazelnut colour
Do not allow the butter to burn as it will become bitter
Remove the pan from the heat and set aside in a warm place
In a large bowl whisk together the eggs, sugar and vanilla until creamy
Add the flour, whisk until smooth, then slowly incorporate the milk, cream, salt and brown butter
Pour the batter into the prepared baking dish
Place the figs cut side up in the batter
Bake in the oven for 30-35 minutes, or until the top is slightly domed and a skewer inserted in the middle comes out clean
To finish, sprinkle with caster sugar and serve warm with the leftover cream softly whipped