Preheat oven 350 degrees F. and lightly oil an 8×8-inch square baking pan.
Prepare the flax egg by combining the ground flaxseed with the water, stir, and set aside and allow it to thicken.
In a medium bowl, whisk together all of the dry ingredients – sugar, baking powder, salt, instant espresso, cocoa powder, and flour and set aside.
Using a double boiler, melt the butter by continuously stirring and then remove from the heat and add in the chocolate and stir until it is melted and smooth.
Pour the chocolate mixture over the flour mixture and slowly stir in the flax egg until the mixture becomes thick.
Stir in the vanilla and cognac and the mixture will become much thinner; continue to stir until everything is combined.
Pour the batter into the baking pan, and bake for 35 to 40 minutes, until a cake tester come out clean.
Allow the brownies to cool for at least 10 minutes before cutting.