To prepare the egg replacement - add the ground flax seed and milk to a small bowl. Whisk to combine and set aside to thicken- 10 to 15 minutes, stir occasionally.
Preheat the oven to 350F and prepare am 8x8 baking pan by lining it with parchment paper.
In a small bowl, combine the flour and baking powder, whisking and set aside.
Once the flax "egg" is ready, add it to a medium bowl along with the cane and coconut sugar. Whisk for one minute and then set the mixture aside.
Put the dark chocolate (100 grams), butter, cocoa powder, and espresso powder in a small pot. Heat over medium, stirring occasionally, until the chocolate and butter melt. Take the pot off the heat and stir until everything is fully combined.
Pour the chocolate mixture into the sugar and flax mixture, add the vanilla, and whisk for a minute until everything is fully blended.
Add the flour mixture to the wet ingredients and fold together until just about combined. Stir in the walnuts and chocolate chips, gently mixing until no streaks of flour remain.
Pour the batter into the prepared pan and sprinkle the reserved walnuts and chocolate chips over the top of the batter.
Bake the brownies for 28 minutes or until a toothpick inserted comes out with minimal crumbs on it.
Let the brownies completely cool in the pan.
Store the brownies in an airtight container at room temperature.