In a medium heatproof bowl, combine butter, unsweetened chocolate and 1/2 cup of chocolate chips. Place the bowl over a saucepan of simmering water and stir until the ingredients are melted and smooth. Remove bowl from heat and let cool.
In a medium bowl, whisk egg and sugar until thickened, then slowly whisk in the melted chocolate, salt, vanilla and flour.
Divide the batter between two individual baking dishes. Bake for 15 to 20 minutes, or until the top is crisp. Let cool. Serve with vanilla ice cream.