In this order, add the dry ingredients and milk to the wet: dry, milk, dry. Whisk each addition until just combined.While whisking, pour in the melted chocolate/espresso mix. Whisk everything until smooth, almost glossy and well combined.
Pour the batter into a prepared 6X2 or 6X3 (preferred) cake pan. The batter will be runny. Bake at 350F (177C) on the center rack of the oven for 35-40 minutes.Cool the cake in the pan placed on a cooling rack for 10-15 minutes. Remove from the pan to cool completely.
In a stand mixer beat butter until light and fluffy, about 4-5 minutes. On the lowest speed, beat in the tahini with butter until well combined. Beat in the powdered sugar, vanilla extract and salt on low-medium speed until well combined.
Apply a light crumb coat the the completely cooled chocolate cake. Chill the cake in the fridge for 15-20 minutes. Apply a thicker final layer of buttercream to the cake as desired. Top with chocolate shavings and/or chocolate sprinkles.