Preheat oven to 350 degrees.
Lightly oil an 8-inch cake pan.
In a bowl, sift together unbleached flour, sugar, baking soda, and Dutch process cocoa.
Puree the beet in a blender or food processor. Pour in coffee and process just until the mixture reaches a creamy, milkshake-like consistency.
Add about half the flour mixture, blitz briefly to combine, then add the oil, vinegar, plantbased milk and vanilla. Process again briefly.
Add the remaining flour mixture and process one last time till it coalesces and forms a thickish, luscious batter.
Pour into the prepared cake pan. Bake for 45 minutes, or until kitchen smells chocolatey and a tester inserted in the cake comes out clean. Cool and unmold.