Preheat the oven to 350°F and grease an 8-inch round metal cake pan with a small amount of oil, then line the bottom with parchment paper.

Whisk the flour, sugar, cornstarch, baking powder, baking soda, and salt together in a large bowl.

Stir the brown sugar, flour, coffee powder, oil, cardamom, and salt together in a small bowl until the topping is evenly combined.

Stir the soy milk, applesauce, oil, lemon juice, vanilla, and water together in a separate bowl and let the mixture rest for a few minutes—it will likely look curdled, which is expected for the proper leavening reaction.

Pour the wet ingredients into the dry ingredients and fold gently with a spatula until just combined; some small lumps are fine, but do not overmix or the crumb will be tough.

Pour half of the batter into the prepared pan and sprinkle with half of the brown sugar topping, then top with the remaining batter and the rest of the topping, swirling a toothpick through the batter a few times to marble the coffee layer.

Bake until the top is golden brown and a toothpick inserted in the center comes out clean, about 35 minutes.

Rest the cake in the pan for 5 minutes before transferring to a wire rack to cool for 1 hour, allowing the structure to set before slicing.