Preheat oven to 350 degrees F (175 degrees C). Grease and flour a Bundt pan.
Combine 1/2 package of vanilla pudding mix with 1 cup of milk in a bowl, and set aside.
Place 1/2 package of vanilla pudding mix, cake mix, vegetable oil, eggs, 1 cup of milk, cinnamon, coffee liqueur, and 1 tablespoon instant coffee granules into a mixing bowl. Beat with an electric mixer on low until just combined, about 30 seconds, then beat on high for 2 minutes. Gently fold in the chocolate chips.
Pour half the batter into the prepared cake pan. Spoon the vanilla pudding in an even layer over the top of the batter, sprinkle with 1/2 tablespoon of instant coffee granules, and cover with the rest of the batter.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, 40 to 45 minutes.
Let the cake cool in the pan for 5 minutes, and invert onto a plate. Cool for 5 more minutes, and dust with confectioners' sugar.
