Preheat oven to 350 degrees F (175 degrees C). Lightly grease an 8-inch square baking dish.
Combine chocolate and butter in top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until chocolate is melted, about 5 minutes. Remove from heat.
Whisk 1 cup plus 1 tablespoon sugar and vanilla extract into melted chocolate mixture. Add eggs, one at a time, mixing well after each addition. Sift 1/2 cup plus 1 tablespoon teff flour and cocoa powder over mixture and mix well until all ingredients are incorporated into a smooth batter. Pour batter into prepared baking dish.
Bake in the preheated oven until a skewer inserted into centre of brownies comes out clean, about 40 minutes. Allow to cool for 10 minutes before slicing into squares.