The cake was inspired by one in Cook’s Illustrated. My addition of laban (yogurt) in the cake adds moistness and a tender crumb; in my mom's buttercream, it adds a tang and depth I love, so good with all of the sweetness.
Heat the oven to 325 degrees. Line muffin tins with 18 paper cups.
In a large bowl, whisk the sugar, flour, baking soda, and salt.
In a liquid measuring cup, stir together the yogurt and milk. In small saucepan, combine the yogurt mixture with the chocolate and cocoa. Cook over medium heat, whisking until the chocolate melts and the mixture is smooth. Remove from heat to cool for about 5 minutes.
Whisk oil, eggs, and vanilla into chocolate mixture (mixture may initially look curdled) until smooth and homogeneous. Add this to the sugar mixture and whisk until combined.
Pour the batter into the lined tins to about ¾ full per cupcake. Bake until the center of the cupcakes springs back when lightly pressed and a toothpick inserted in center comes out with a few crumbs attached, 20 to 25 minutes. Cool the cupcakes before frosting.
For the buttercream, in a medium bowl, work the butter and cocoa together using the back of a large spoon until completely combined. Add the confectioner’s sugar one cup at a time, alternating with the yogurta tablespoon at a time to moisten. Add the vanilla and stir until smooth.