Chop chocolate into small pieces if using a bar. Heat a small pan with an inch of water in the bottom until water simmers. Place a pan on top of it that completely covers the bottom pan. Place chocolate in the top pan and stir until just melted and smooth. Remove from heat and let cool 5 minutes.
Crumble tofu into a blender. Add soy milk, Kahlua, syrup, and vanilla. Puree until smooth.
When chocolate is cool, add it to the tofu puree. Blend until combined.
Pour into a bowl or airtight container, cover, and refrigerate at least one hour.
After chilling, I whipped the frosting in my stand mixer with the whisk attachment so it was fluffier.