Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper and set aside.

In the bowl of a stand mixer fitted with the paddle attachment (or using an electric hand mixer), cream together the softened butter and granulated sugar on medium speed until light, fluffy, and smooth, about 2–3 minutes.

With a rubber spatula, scrape down the bottom and sides of the bowl. Add the slightly chilled egg and mix on medium speed for about 20 seconds, just until incorporated. Add the cold egg yolk, scrape down the sides again, then add the vanilla extract and mix on low speed until fully combined and smooth.

Add the flour, Dutch-processed cocoa powder, baking soda, baking powder, cornstarch, chopped chocolate, and salt. Mix on low speed until the dry ingredients are just incorporated and no dry streaks remain. Be careful not to overmix.

Scoop the dough into 4 tablespoon portions and gently flatten each scoop into a thick disk.

Spoon 1–2 teaspoons of marshmallow fluff into the center of each portion, then carefully bring the dough up and around the marshmallow, rolling into a ball. Leave a small amount of marshmallow visible on top for that gooey finish.

Place the dough balls on the prepared baking sheets, spacing them 2–3 inches apart.

Bake for 10 minutes, until the edges are set and the centers still look soft and slightly underbaked.

Remove the cookies from the oven and immediately press pieces of chocolate and broken graham crackers into the tops of each warm cookie so the chocolate melts slightly into the surface.

Sprinkle lightly with flaky sea salt and additional graham cracker crumbs if desired, then let the cookies cool on the baking sheet for about 10 minutes before serving.