In a mixing bowl stir together flour, sugar, cocoa, salt, and baking soda.
In a smaller bowl combine the vegetable oil, water, and vinegar. Stir to combine.
Pour the water mixture into the flour mixture. Stir until combined.
Spoon half of the batter equally amongst the prepared ramekins. Place one of the chilled chocolate balls in each dish and cover with the remaining chocolate batter.
Place the baking sheet with filled ramekins in the heated oven and bake for 20 minutes or so, until the tops are just set. Let cool 2 to 3 minutes.
When the ramekins are cool enough to handle, run a knife around the inside edge to release the cake from the ramekin. Turn the ramekin over onto a dessert plate, and dust with powdered sugar. Top with your favorite fresh berries, like raspberries. I suggest serving these immediately, but they do well the next day, too.
To store, let the cakes come to room temperature. Transfer to an airtight container and refrigerate for up to 7 days. They can be frozen in a freezer-safe container for up to 2 months.