Heat oven to 350° F. Line 2 baking sheets with parchment. In a large bowl, whisk together the flour, salt, baking powder, and baking soda; set aside.
In a large microwave-safe bowl, combine the butter and half the chocolate. Microwave on high, stopping and stirring every 30 seconds, until melted and smooth; let cool slightly. Whisk in the sugar, eggs, and vanilla until smooth.
Gradually add the flour mixture, mixing until just combined (do not overmix). Fold in the marshmallows and the remaining chocolate. Let cool for 15 minutes.
Drop mounds of the dough (about 1 heaping tablespoon each) 2 inches apart onto the prepared baking sheets.
Bake, rotating the baking sheets halfway through, until firm around the edges and cracked on the tops, 12 to 15 minutes. Let cool slightly on the baking sheets, then transfer to wire racks to cool completely.