Preheat the oven to 350° and line 4 muffin cups with paper liners.
In a medium heatproof glass bowl set over a saucepan of simmering water, combine the chocolate chips with the butter, sugar, cornstarch and vanilla. Stir until the chocolate chips are melted and smooth.
Remove the bowl from the saucepan and let the chocolate mixture cool slightly. Whisk in the whole eggs and the egg yolks.
Spoon the batter into the lined muffin cups. Bake for 10 minutes, until set around the edges and soft in the center. Let stand for 5 minutes.
Meanwhile, in a small bowl, whisk the apricot jam with the Cognac until smooth.
Invert the cakes onto plates and remove the paper liners. Spoon the apricot-Cognac sauce around the cakes and serve.