In a large bowl, whisk together flour, cocoa powder, baking powder and salt, and reserve.
Chop 12 ounces of semisweet chocolate into 1/2-inch pieces. In a double boiler over gently simmering water, melt butter and chopped chocolate, whisking frequently, until smooth. Remove from heat and cool 15 minutes.
In a bowl of an electric mixer on medium speed, beat brown sugar, eggs and vanilla extract until smooth, about 2 minutes. Add melted chocolate mixture and mix until just blended. Reduce speed to low and add flour mixture in 2 batches, mixing until just combined. Cover with plastic wrap and refrigerate at least 1 hour.
When ready to bake, preheat oven to 325 degrees and line baking sheets with parchment paper. Break remaining 4 ounces of chocolate into small pieces, and cut marshmallows (if necessary) into a size suitable for the top of the cookie.
Roll dough into 1-inch balls. Place dough 2 inches apart on prepared baking sheets, flattening dough slightly. Bake until tops of cookies crack, about 12 minutes. Remove from oven and gently press a chocolate piece, then a marshmallow (or 3 minis), onto each cookie. Return cookies to oven and bake until marshmallows are just softened, about 4 minutes. Remove from oven and cool 5 minutes before transferring cookies to a wire rack. Grate remaining chocolate over warm cookies as a garnish.