In a medium saucepan, melt together:
1 stick (4 ounces) unsalted butter
1 1/2 cups flour
1 1/2 teaspoons baking powder
1/4 teaspoon salt
1 1/4 cups light brown sugar
1 1/2 teaspoons pure vanilla extract
Beat on low speed until smooth, 2 minutes. Mix in the cooled chocolate mixture just until blended. Add the flour mixture in 2 batches, mixing on low speed until just combined. Refrigerate the dough for at least 1 hour.
Preheat the oven to 325 degrees F. Line 2 large baking sheets with parchment paper. Using a tablespoon, scoop the dough and roll between your palms to form 1-inch balls. Arrange about 16 balls 2 inches apart on each cookie sheet, flattening slightly. Bake until the tops of the cookies crack, about 12 minutes.
Meanwhile, cut 7.5 ounces of semisweet chocolate (bars) into 1-inch squares. Snip 8 marshmallows in half crosswise and stick 1 square of chocolate onto each of the cut sides.
Remove the cookie sheets from the oven and gently press a marshmallow half, chocolate side down, into each cookie. Bake until the marshmallows are just softened, about 4 minutes. Transfer the pans to racks to cool for 5 minutes.
Grate 5 ounces of semisweet chocolate over the hot cookies. Using a spatula, transfer the cookies to the racks and let cool. Repeat the process with the remaining dough, marshmallows and chocolate. Bake each batch on a clean sheet of parchment paper.