Using the handle of a wooden spoon or rubber spatula poke holes, approximately 2-inches apart, into your pre-baked cake (making sure not to poke all the way through). If using a pre-baked bundt, poke holes in the underside (flat side) of the bundt. Set aside.
Place vanilla pudding mix and 2 cups of whole milk in a large bowl and whisk to combine. Before the pudding has a chance to firmly set, pour over the cake, gently tapping the cake pan to encourage the pudding into the holes.
Cover and refrigerate the cake for 10-15 minutes (just enough time for the pudding to firm).
Meanwhile, place 4 tablespoons of whole milk, chocolate chips, and sweetened condensed milk in a large bowl.
Fill a large pot or saucepan 1/4-full with water and bring to a low simmer over medium-low heat (a pot or saucepan large enough to nestle the bowl, creating a double boiler).
Place the bowl over the simmering water and stir. Continue to stir the contents until the chocolate has melted completely creating a thick ganache, about 5-8 minutes.
Remove the bowl from the heat and set aside to cool briefly, about 2-3 minutes.
Drizzle the ganache over the cake and set aside to harden and cool at room temperature for 15-30 minutes before slicing and serving.