Microwave ONE CUP of the semisweet chocolate morsels in a small microwave-safe glass bowl at HIGH 1 minute or until smooth, stirring every 30 seconds.
Beat butter and sugar at medium speed with an electric mixer until creamy; add eggs, 1 at a time, beating until blended after each addition. Gently beat in vanilla, then the melted chocolate.
Combine flour, baking powder, and salt; whisking together in a small bowl. Gradually add to flour mixture to the chocolate mixture, beating until well blended.
Stir in remaining semi sweet chocolate chips.
Drop dough by heaping tablespoonfuls (my cookie scoop worked perfectly) onto parchment paper-lined baking sheets. Press 3 marshmallows into each portion of dough.
Bake at 350° for 10 to 12 minutes (10 minutes was perfect for mine) or until set. Let cool on cookie sheet for a few minutes to allow them to rest and deflate a bit, then remove to wire racks to cool completely.