Place 1 1/2 tablespoons chocolate chips and heavy cream in a small bowl with espresso powder. Microwave for 45 seconds and stir until smooth. Refrigerate for 30 minutes.
Preheat oven to 425°. Coat ramekins with butter and sprinkle with cocoa powder, tapping out excess.
Combine butter and remaining chocolate in a medium heatproof bowl and microwave for 30 seconds, stir. Repeat until the chocolate is just melted.
Using a whisk, beat eggs and brown sugar in a large bowl until light and tripled in volume. Mix in vanilla.
Gently fold melted chocolate into egg mixture until incorporated. Fold in flour and salt, stirring until smooth.
Put half of the batter in each of the two 6-8 oz ramekins. Place half of the ganache in the center of each partially filled ramekin and top evenly with remaining batter.
Bake until edges are firm and cakes wobble slightly when jiggled, 13–15 minutes. As soon as the ramekins are cool enough to touch, invert onto small plates and serve immediately with whipped cream and berries, if desired.
My favorite way to eat these cakes is straight from the oven, still in the ramekin, topped with a massive amount of whipped cream and raspberries.