Preheat oven to 350°F. Line the bottom of an 8-inch round cake pan with parchment paper, and grease the paper and sides of the pan.
In a large bowl, use a hand or stand mixer to beat the ½ cup unsalted butter¾ cup packed light or dark brown sugar, and 2 tablespoons granulated sugar until fluffy; scrape down bowl. Add the 1 large egg, 1 large egg yolk, and 1 teaspoon pure vanilla extract, and beat until combined. Add the ¼ cup whole fat plain yogurt or Greek yogurt and ½ cup strong coffee and mix until well combined.
Place a sifter over the bowl and in the 1 cup teff flour, ½ cup unsweetened cocoa powder, ½ teaspoon baking powder, ¼ teaspoon baking soda, and ½ teaspoon fine sea salt, then sift it into the bowl.
Beat in the flour mix on low until just combined, and scrape down the bowl a final time.
Pour the batter into the prepared pan and smooth the top using a rubber spatula. Rest the batter for 20 minutes, then place the cake in the oven and bake for 30-35 minutes, until a toothpick inserted into the center comes out clean and the top is set.
Place the cake on a wire rack to cool for 20 minutes in the pan, then turn out onto the rack to cool completely.
Frost the top with chocolate buttercream frosting.