Prepare to bake. Preheat the oven to 350 degrees F. Line an 8-inch baking pan with 2 pieces of parchment paper, going opposite ways, leaving enough paper to cover the sides and hang over the edges. Grease the paper. Melt the butter and chocolate. Put the butter and chocolate in a microwave-safe bowl. Microwave for 1 minute. Whisk together the melted butter and chocolate. If there are any remaining chunks of chocolate, microwave for 30 seconds more. Stir well.
Make the batter. Let the butter-chocolate mixture sit until it is cool to the touch. Add the sugar and stir until it is dissolved. Add the eggs, one at a time, stirring between each addition. Stir in the vanilla. Add the teff flour and stir the batter thoroughly with a rubber spatula for at least 1 minute. Toss in the hazelnuts and chocolate chips and stir until just combined.
Bake the brownies. Pour the batter into the prepared pan and spread it evenly into the corners. Bake until the edges have begun to pull away from the pan and the center is just starting to set, 20 to 25 minutes. Cool the brownies in the pan for at least 15 minutes. Using the overhanging parchment as handles, lift the brownies out of the pan; cool the brownies on a cooling rack. Remove the parchment and dig in.