Preheat the oven to 375F. Butter 24 barquette tins (oval tins with pointed ends) or a mini muffin tin and place them on a baking tray, or grease mini muffin cups with butter and chill the pan while preparing the batter.
Stir the ground almonds, flour, sugar, and cinnamon together. In a separate bowl, whisk the egg whites by hand just until they are foamy. Add the whites to the almond mixture and stir until blended. Add the almond extract, then stir in the currants and the melted butter (the batter will be runny).
Spoon the batter into the prepared tins and bake for 15 to 18 minutes, until the centres of the financiers peak and the outside edges are golden brown. Cool the financiers in their tins before removing.
The financiers will keep for 5 days in an airtight container.