Coat the inside of 4 1-cup (125 G) ramekins with softened butter, then sprinkle with the granulated sugar, tilting to coat completely. Set aside on a rimmed baking sheet.
Heat the heavy cream in a small pot until boiling.
Pour the boiling cream over ½ cup (120 ml) dark chocolate in a small bowl and let sit for 3 minutes. Stir until the chocolate is melted and smooth. Refrigerate for at least 30 minutes, or store in the freezer for up to 3 months.
Preheat the oven to 425°F (220°C).
In a small microwave-safe bowl, combine the remaining ¾ cup (170 G) chocolate and the butter. Microwave in 30-second intervals, stirring between, until completely melted.
In a medium bowl, beat the eggs, egg yolks, brown sugar, salt, and vanilla with an electric hand mixer on medium-high speed until light and frothy, about 8 minutes.
Gently fold the chocolate mixture into the egg mixture, being careful not to deflate the eggs. Add the flour and fold to incorporate.
Divide half of the batter between the prepared ramekins. Add ½ tablespoon of the chilled ganache to the center of each ramekin, then scoop the remaining batter on top.
Bake for 12 minutes, until the tops are set and the cakes begin to pull away from the sides of the ramekins.
Let the lava cakes cool slightly, then invert onto plates. Dust with powdered sugar and garnish with berries. Serve immediately.