Add the vegan chocolate to a microwave-safe bowl. Microwave in 30-second intervals, bringing it out to stir every 30 seconds until melted. Leave it to cool.
Sift the all-purpose flour and cocoa powder into a separate mixing bowl and mix in the espresso powder, baking powder, and salt. Set aside.
To the bowl of your stand mixer, add the vegan butter and brown and white sugar and cream for 2 minutes. The mixture should be light and fluffy.
Add the vanilla extract and beat in.
Now add the cooled chocolate and beat in for another 2 minutes.
Pour the dry ingredients into the wet and mix in by hand until crumbly.
Add the soy milk or other non-dairy milk and mix it into a thick cookie dough.
Add the chocolate chips and fold them in. Your cookie dough should be very thick, but still sticky enough to roll into balls.
Roll into balls and space them evenly over two parchment-lined baking sheets. Aim to get 20 cookies from the batch, 10 cookies per baking sheet. Chill your cookies in the freezer for 15 minutes while the oven preheats.
Preheat the oven to 350°F(180°C).
Bake for 10 minutes. If the cookies are still very puffy when they come out of the oven, then you can gently flatten them with a fork while they are still soft and warm.