Preheat oven to 350 degrees F, and adjust rack to middle position. Butter an 8-inch glass square pan. Place butter and chocolate in the bowl of a double boiler. Melt over low heat. Remove chocolate mixture from heat and whisk in sugar, sea salt, and vanilla extract.
Whisk in eggs one at a time. Whisk in tapioca flour and coconut flour. Let batter sit for 5 minutes (this allows the coconut flour to absorb some of the moisture). Pour batter into the buttered baking dish and smooth into an even layer. Bake for 25-30 minutes until edges are just pulling away from the sides and middle is still just a touch moist. Cool and then cut into squares. Store in an airtight container for up to three days.