Combine the dry ingredients. In a medium bowl, whisk together the flour, Dutch-process cocoa powder, instant coffee powder, baking soda, and salt.
Cream the butter and sugars. In a large bowl, beat the softened butter, granulated sugar for about 2 minutes, until creamy.
Add the egg and vanilla. Beat in the egg and vanilla until smooth and combined.
Make the dough. Gradually add the dry ingredients to the wet ingredients. Mix just until a thick chocolate cookie dough forms.
Prepare for baking. Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
Shape the cookies. Scoop about 2 tablespoons of dough and roll into balls and press them slightly. Place them about 2 inches apart on the prepared baking sheet. Gently flatten the tops slightly.
Bake. Bake for 10–12 minutes, until the edges are set and the centers still look slightly soft. Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack and cool completely before decorating.
Melt the marshmallows. Place the jumbo marshmallows in a microwave-safe bowl. Microwave for about 15–20 seconds, just until puffed and melted. Stir carefully.
Create the spider webs. Allow the melted marshmallow to cool just enough to handle. Lightly grease your fingertips with a tiny amount of neutral oil or cooking spray. Pick up a small amount of melted marshmallow between your fingers, pull your fingers apart to create thin strands, and gently stretch the strands across the cooled cookies.
Set the webs. Repeat in different directions until each cookie has an irregular spider-web pattern. Allow the marshmallow to set before serving.