Special equipment: four 4-ounce ramekins
For the cassis berries: Put the cassis in a small saucepan and bring to a boil over medium-high heat. Boil until reduced to about 3 tablespoons, about 5 minutes. Put the berries in a bowl and toss with the reduced cassis. Let stand, stirring occasionally, about 1 hour.
For the cake: Preheat the oven to 400 degrees F. Butter four 4-ounce ramekins and dust with the cocoa powder.
Put the butter in a small saucepan and heat over low until melted. Add the chocolate, espresso powder, vanilla and salt and stir until thoroughly melted and combined. Stir in the flour.
Combine the sugar, whole eggs and yolks in a large bowl and beat with an electric mixer on high speed until pale and thick, about 3 minutes. Add the chocolate mixture to the beaten eggs and beat to combine. Divide the mixture among the ramekins (at this point, the cakes can be refrigerated up to 4 hours and then brought to room temperature before baking).
Put the ramekins on a baking sheet and bake until the tops and edges are set but about an inch in the center is still wobbly, about 12 minutes. Let the cakes stand for 1 minute. Run a thin knife around the edge of the cakes. Cover a ramekin with a small plate and invert the ramekin (using an oven mitt or towel) onto the plate. Remove the ramekin, leaving the cake on the plate. Repeat with the remaining cakes.
For the berry mascarpone: Transfer 3 tablespoons of the berry juices from the cassis berries to a bowl. Add the mascarpone, sugar and vanilla and mix to combine.
Dollop the berry mascarpone on the cakes and top with a spoonful of the cassis berries. Garnish with mint sprigs.