Preheat the oven to 350 degrees F (175 degrees C). Grease and flour an 8-inch round cake pan.
Combine flour, sugar, cocoa powder, baking soda, and salt in a large bowl, whisking until smooth. Cut in buttery spread using a pastry cutter or 2 knives until it is the size of small peas and flour mixture is evenly coated.
Pour soy milk, coffee, vinegar, and vanilla extract into the bowl. Blend with an electric mixer until smooth; beat for 2 minutes more. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 35 to 40 minutes. Cool in the pan for at least 10 minutes before inverting onto a wire rack or serving plate.
Substitute another vegan milk for the soy milk if preferred.
You can use another type of vinegar in place of apple cider vinegar.