Preheat oven to 350F and prepare an 8x8 baking pan by lining it with a sheet of aluminum foil, leaving a few inches of overhang on the sides to allow for easy removal.
Add coconut oil and chocolate chips to a small microwaveable bowl. Heat for 1 minute at half power. Stir and continue to heat for 15 seconds at a time at full power until chips are melted. Set aside.
Using a handheld mixer or a stand mixer fitted with the whisk attachment, beat together eggs, sugar, and vanilla extract until smooth about 2 minutes. Add melted chocolate mixture and mix until well combined. Reduce speed to low and add cocoa powder, almond flour, arrowroot powder, and salt, mixing until well combined and scraping down the sides of the bowl as necessary. Batter should be thick and smooth.
Pour batter into pan, spreading it evenly with a spatula. Bake for 25-30 minutes.
Remove from oven and transfer brownies in the foil to a wire rack to cool completely. Cut into squares and serve.