Combine oil, eggs, sugars, and vanilla in a bowl. Add the cocoa, starch, baking powder and salt. Mix well. Stir in the chocolate chips and marshmallows.

Refrigerate overnight for best results or at least several hours to firm up.

When ready to bake, preheat your oven to 350 degrees Fahrenheit and prepare two parchment-lined baking sheets. Use a one-fourth-cup measuring cup to portion the batter, placing no more than five tall mounds of dough on each baking sheet, leaving room for them to spread. Add a few marshmallows and pieces of Graham crackers to the surface of each cookie, pressing into the batter slightly. Bake for 15 minutes.

Allow to cool on the parchment before removing.