Melt the butter in a pale saucepan over medium heat. Cook until foaming and the milk solids turn golden. Cool 10 minutes.
Preheat the oven to 170C fan. Grease and line a 20cm round cake tin.
Whisk the browned butter and caster sugar together. Beat in the eggs one at a time, then the almond extract.
Fold in the ground almonds, flour, baking powder and a pinch of salt. Spoon into the tin and level.
Nestle the plum halves cut-side up into the batter. Scatter with flaked almonds and demerara sugar.
Bake 40-45 minutes until golden and a skewer comes out clean.
Cool in the tin 15 minutes, then transfer to a rack. Serve slightly warm with creme fraiche.
Tap to reveal the secret seasoningAlmond extract – one teaspoon makes the plums taste more intensely fruity and reinforces the toasted flavour of the brown butter and almonds.