Preheat the oven to 350°F. Cover the bottom of a 9-inch-round cake pan with parchment paper. Cut a strip to fit around the sides; place the strip inside the pan, holding it in place with a clip or clothespin if necessary. Set aside.

Melt chocolate in the top of a double boiler placed over simmering water, stirring occasionally until smooth. Set aside to cool.

In a blender, combine almond milk, apple sauce, dates, espresso powder and vanilla. Blend until smooth, 1 to 2 minutes. In a bowl, whisk together the flour, cocoa powder, baking powder, baking soda and salt. Pour in date mixture and stir just until combined. Stir in chocolate. Pour the mixture into the prepared pan (remove the clip or clothespin).

Bake in the middle of the oven until a toothpick inserted in the center comes out with just a few crumbs clinging to it, about 30 minutes. Cool the cake in the pan on a rack.

Run a knife around the edge and invert the cake onto a platter. Remove the paper.