Whisk the butter and sugar together in a medium mixing bowl until well combined. Whisk in the vanilla and melted chocolate. Add the egg and whisk until fully combined.

Stir the flour, cocoa powder, salt, baking soda, and espresso powder (if using) together in a second medium bowl. Stir the dry ingredients into the butter-chocolate mixture with a wooden spoon; if the dough is too stiff to mix with the spoon, use your hands. Mix until the dough is cohesive. Let the dough sit at room temperature for 1 hour.

Transfer the dough to a large square of parchment paper and shape into a log about 10 inches long. Wrap the parchment around the log, then roll back and forth on the counter a few times to form a smooth log of dough. Place in refrigerator for at least 2 hours, turning the log every 15 minutes or so to maintain the log’s round shape.

Center a rack in the oven and preheat to 325 degrees. Line two large baking sheets with parchment paper.

Cut the dough into 1/4-inch-thick slices and arrange them on the prepared baking sheets 1 inch apart. Bake for 18 to 23 minutes, just until cookies are firm to the touch. Cool cookies completely on the baking sheets before filling.

Place the butter in the bowl of a stand mixer fitted with the paddle attachment. Beat on low speed until very smooth, about 30 seconds. Beat in the powdered sugar, cake mix, vanilla, milk, and salt and mix until mixture is very smooth. Fold in the rainbow jimmies with a rubber spatula.

Scoop 1 heaping tablespoon of filling onto half of the cookies. Top with remaining cookies, then press down to flatten the filling. Serve and enjoy.