Preheat the oven to 350°F (177°C). Brush the bottom and sides of an 8x8” baking pan with oil and line with parchment paper. Set aside.
Using the double boiler method or in a microwaveable bowl, melt together the dark chocolate chunks and coconut oil. Be sure to stir occasionally to ensure the chocolate doesn't burn at the bottom. If using a microwave, only heat up 30 seconds at a time. Once it has melted, give it a nice stir and set aside to cool.
In a separate large mixing bowl, add eggs, milk, coconut sugar, cacao, arrowroot, salt, vanilla, and peppermint extracts. Mix well with a fork or use a hand mixer to blend everything together until smooth throughout, about 30 seconds. Do not over mix.
Once the chocolate/oil mixture is warm to the touch (but not hot), add it to the large mixing bowl. Fold several times using a spatula until smooth throughout. This will take about 1 minute.
Pour the batter into the prepared baking dish and smooth over with an offset spatula. Tap on the counter a few times to release air bubbles. Bake at 350°F for 24-28 minutes. Remove from the oven and let cool in the pan for about 15-20 minutes before carefully removing from the pan.
Once they are cool to the touch, use an offset spatula to spread on the chocolate topping. Top off with crushed candy canes if you'd like and let the brownies set in the refrigerator for about 1 hour before carefully slicing and serving.
These can be stored in an airtight container at room temperature for up to 2 days or up to 5 days in the refrigerator.