Preheat your oven to 350°F. Line an 8 x 8 pan with parchment paper or tin foil, leaving some overhang for easy removal. Lightly grease and set aside.
In a microwave-safe bowl or using a stovetop, melt the chopped chocolate with the coconut oil until just combined. Remove from heat.
Whisk the sugar into the chocolate mixture. Add the eggs one at a time, whisking each one in. Then, add the cocoa powder and arrowroot powder, and whisk until the batter is smooth and no longer grainy.
Pour the brownie batter into the prepared pan. Bake for 20-25 minutes, or until a toothpick inserted in the center comes out mostly clean. Avoid over-baking.
Let the brownies cool completely in the pan. Once cooled, slice into 9 pieces.