Preheat the oven to 350°F and lightly oil six (4 ounce) ramekins. (Note 1)
Place the dates into a blender or the bowl of a food processor fitted with an s-blade. Carefully pour the just-boiled water over them and add the apple cider vinegar. Let the dates soak for 5 minutes. (Note 2)
Blend the dates until smooth. Set aside.
Stir the milk and flaxseeds together in a small bowl or container. Let the mixture sit for about 5 minutes to gel.
While the flax mixture sits, whisk the flour, baking powder, baking soda, and salt together in a large mixing bowl.
In another large mixing bowl, cream the butter and brown sugar together using an electric mixer at high speed. Beat in the vanilla.
Add the flax mixture to the bowl and continue beating the mixture for one full minute, until it becomes creamy and pale.
Add the date mixture to the bowl and beat it in, just until fully blended.
Begin beating the flour mixture in, adding it in two to three increments and beating each in at low speed.
Divide the batter among the ramekins. Place the ramekins on a baking sheet, and then place the baking sheet into the oven.
Bake the cakes until they've puffed up and a toothpick inserted into the center of one comes out clean, about 25 to 27 minutes.
Place the baking sheet on a cooling rack and let the cakes cool completely. The cakes will fall slightly as they cool.