Preheat oven to 350 degrees. Spray a 9X13-inch baking dish with cooking spray.
For the topping, whisk the sugar and cocoa powder together until well-combined. Set aside.
For the cake, whisk the flour, sugar, cocoa powder, baking powder, and salt in a large bowl.
To the dry ingredients, add the milk, butter, egg yolks, and vanilla and whisk together until just combined.
Add the chocolate chips and stir to combine evenly; the batter will be fairly stiff.
Spread the cake batter evenly in the prepared pan. Sprinkle sugar/cocoa topping evenly over the top of the cake batter.
Carefully pour the boiling water over the top. Do not stir.
Immediately bake the cake until the top is puffy and slightly cracked, sauce is bubbling and a toothpick inserted into cakey area comes out with moist crumbs attached, about 22-25 minutes. Over baking may result in a very thin or nonexistent pudding layer, so keep an eye on the baking time.
Cool the cake for 10-15 minutes. Serve warm with vanilla ice cream.