In a medium saucepan, melt the butter and chocolate chips, stirring frequently, over medium heat. Remove from heat and let cool for 15 minutes.
In a medium bowl, whisk together the flour, cocoa powder, baking powder and salt.
In a large bowl, using an electric mixer, beat the sugar, eggs and vanilla at low speed just until smooth and combined. Mix in the cooled chocolate mixture just until blended. Add the flour mixture in 2 batches, mixing on low speed until just combined. Cover and refrigerate the dough for at least 1 hour.
Line 2 large cookie sheets with parchment or wax paper. Using a cookie scoop or 2 Tablespoon measuring spoon, scoop the dough and roll between your palms to form cookie balls. Arrange about 15 balls, an inch or so apart on each cookie sheet. Bake at 325 degrees F. for 12 minutes or until the tops of the cookies crack.
Meanwhile, cut marshmallows in half crosswise and stick 1 piece of chocolate onto each of the cut sides.
Remove the cookies from oven; gently press a marshmallow half, chocolate side down, into each cookie. Place back in oven and bake until the marshmallows are just softened, about 4 minutes. Remove from oven; let cool 15 minutes before serving.