For the cake: Preheat the oven to 350 degrees F. Butter and line an 8-inch square baking pan with parchment paper, leaving a 2-inch overhang on two sides.
In a large bowl, whisk together the flour, baking powder and salt. In another large bowl, using an electric mixer on medium speed, beat the butter and sugar until fluffy, about 2 minutes. Beat in the eggs, one at a time, and then beat in the vanilla. In three additions, beat in the flour mixture, alternating with additions of the buttermilk, starting and ending with flour. Fold in the chocolate. Transfer the batter to the prepared pan and smooth the top. Bake until a toothpick inserted into the center comes out with moist crumbs attached, 30 to 35 minutes. Transfer the pan to a rack to cool completely, and then remove the cake from the pan using the parchment overhangs to lift it out.
For the frosting: In a large bowl, whisk together the malt powder, cocoa powder and boiling water until smooth. Let cool.
Add the butter and beat with an electric mixer on medium speed until smooth and fluffy. Add the chocolate and salt and beat until smooth and thick. Spread the frosting onto the cooled cake.