Make the cream cheese swirl: In a medium bowl, beat the cream cheese, egg, and sugar until completely smooth and silky, 1–2 minutes. Fold in the chocolate chips. Refrigerate for 10 minutes to firm slightly.
Preheat the oven to 355°F (180°C) and line two 12-cup muffin pans with paper liners.
Prepare the cupcake batter according to the cake mix package directions. Let the batter rest for 2–3 minutes to allow bubbles to settle.
Fill each liner with about 1 tablespoon of chocolate batter. Add 2 teaspoons of the chilled cream cheese mixture to the center, then top with another scant tablespoon of batter. Use a toothpick to give one gentle swirl so a little cream cheese peeks through. Liners should be about 3/4 full.
Bake one pan at a time on the center rack for 17–19 minutes, until the tops spring back and a toothpick inserted into the cake portion (avoid the cream cheese pocket) comes out with a few moist crumbs. Cool in the pan for 5 minutes, then transfer to a wire rack and cool completely before frosting.
Make the frosting: In a small saucepan over low heat, melt the butter. Whisk in cocoa powder and espresso powder until smooth and glossy, 30–60 seconds. Scrape into a mixing bowl. Beat in half the powdered sugar and half the heavy cream on low until combined. Add vanilla and salt, then mix in the remaining sugar and cream. Increase to medium speed and beat for 2 minutes, adding a teaspoon or two more cream if needed for a soft, spreadable consistency.
Finish: Pipe or spread the frosting onto the cooled cupcakes. Garnish with a few extra chocolate chips if you like.