Set a heatproof bowl over a saucepan of barely simmering water. Add the chocolate and stir until melted and smooth. Remove from the heat, add the granulated sugar and brown sugar, and whisk until glossy. Let cool slightly.

In a large bowl, whisk together the soy milk and oil. Add the flour, cocoa powder, baking powder, and salt, and whisk until no dry streaks remain. Whisk in the melted chocolate mixture until the batter is smooth and evenly combined.

Fill each prepared ring one-third full with batter. Spoon 1 tablespoon Biscoff spread into the center of each cake, then cover with more batter until the rings are three-quarters full.

Bake until the edges are set and the centers still tremble slightly, 10 to 12 minutes. Let stand for 1 minute, then serve warm.