Preheat your oven to 350°F (175°C). Grease an 8-inch square baking dish.
In a large mixing bowl, whisk together the flour, sugar, cocoa powder, baking powder, and salt until well combined.
Add the milk, vegetable oil, and vanilla extract to the dry ingredients. Mix until smooth and fully combined.
Pour the batter into the prepared baking dish.
Carefully pour the boiling water over the batter (do not stir). The water will create a pudding layer underneath.
Sprinkle the chocolate chips evenly over the top.
Bake in the preheated oven for 30-35 minutes, or until the top is set and a toothpick inserted in the center comes out mostly clean.
Let the cake cool for about 10 minutes before serving.