In a 3- to 4-quart pan over very low heat, stir chocolate chips and butter until melted and smooth.

Remove from heat and whisk in granulated sugar, eggs, and vanilla until well blended. Stir in flour.

Fill six buttered, floured ramekins (1/2-cup capacity; see notes) about halfway. Press a marshmallow into the center of the batter in each ramekin. Spoon remaining batter equally over marshmallows, completely covering.

Bake in the center of a 350 Fahrenheit regular or 325 Fahrenheit convection oven until tops are puffed up and crackly, 12 to 15 minutes.

Let cool about 10 minutes, then run a knife along inside of ramekins and invert to release cakes.