Prepare cake mix batter according to package directions, adding espresso powder before mixing. Transfer to a greased 4-qt. slow cooker.
In a small bowl, whisk milk and pudding mix 2 minutes. Let stand until soft-set, about 2 minutes. Pour over batter. Cook, covered, on low 3 to 3-½ hours or until a toothpick inserted in cake portion comes out with moist crumbs.
Sprinkle top with chocolate chips and baking chips. Turn off slow cooker; remove insert. Let stand, uncovered, until chips are softened, 15-30 minutes. Serve warm.
