Cream the butter, light brown sugar, and granulated sugar together until light and fluffy, about 2 minutes.
Mix in the egg, egg yolk, and vanilla extract until just combined.
Mix in the flour, cocoa powder, espresso powder, salt, baking soda, and baking powder until just combined.
Cover the bowl and chill the chocolate cookie dough in the fridge for 1 hour.
Preheat the oven to 350 F/180 C.
Scoop 8 dough balls with a standard cookie scoop (two tablespoons) onto a parchment-lined baking tray. Re-cover the bowl of dough and keep it in the fridge while the first tray bakes!
Cut 4 marshmallows in half lengthwise.
Then lightly flatten each dough ball. Place one marshmallow half in the center of the dough. Fold the dough around it so it’s completely encased.
Roll the cookies in the cane sugar, leaving a thicker pile of sugar on top of the cookie.
Bake the cookies for 8-10 minutes, or until the puffy tops are cracked.
Remove and let the tray cool on a wire cooling rack. The marshmallow may make them stick to the pan, use a spatula if needed to keep them from tearing.