In a large bowl, beat the butter, brown sugar and granulated sugar for 2 minutes until fluffy. Beat in the egg and vanilla until smooth.
Whisk the flour, cocoa powder, cornstarch, espresso powder, baking soda and salt in a separate bowl. Mix into the butter mixture on low until combined, fold in the chocolate chips, and chill the dough for 30 minutes.
Preheat the oven to 350°F and line two baking sheets with parchment paper. Scoop the dough into 2 tablespoon balls, place them 2 inches apart, and bake for 8 minutes.
Remove the sheets from the oven and gently press a marshmallow half, cut side down, onto the center of each cookie. Return to the oven for 2-3 minutes, until the marshmallows are puffed and soft.
Let the cookies cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely.
Melt the chocolate chips with the coconut oil in the microwave in 20-second bursts, stirring until smooth. Drizzle over the cookies and let the chocolate set for 15 minutes before serving.