Line a 12-cup muffin pan with paper liners and heat the oven to 350°F (177°C).
Bloom the chocolate: Warm the milk until steaming (not boiling), then whisk in the cocoa powder and espresso powder until smooth and glossy. Let cool 5 minutes.
Make the cheesecake swirl: In a medium bowl, beat the cream cheese and 1/4 cup sugar until creamy. Mix in the egg, vanilla, and lemon zest until silky, then fold in the mini chips. Refrigerate 10 minutes to slightly thicken.
Whisk the dry cupcake ingredients (flour, 3/4 cup sugar, baking soda, and salt) in a large bowl. In a separate bowl, whisk the egg, oil, and vanilla. Stream the warm cocoa-milk mixture into the egg mixture, then pour the liquids over the dry ingredients and whisk just until smooth. Let the batter rest for 5 minutes.
Portion and par-bake: Divide the chocolate batter among liners, filling just under halfway (about 2 tablespoons each). Bake for 4 minutes to lightly set the bottoms.
Top and finish: Remove the pan from the oven and spoon about 1 1/2 tablespoons of cheesecake mixture onto the center of each cupcake. If you like, drag a toothpick once through the cheesecake to nudge it toward the edges. Return to the oven and bake 14 to 17 minutes, until a toothpick inserted into the chocolate portion comes out clean and the cheesecake looks set at the edges with a slight wobble in the center.
Cool in the pan for 5 minutes, transfer to a rack to cool completely, then chill at least 1 hour for the cleanest layers. Store covered in the refrigerator and serve slightly cool or at room temperature.