Preheat oven to 350°F. Grease a 10x15-inch baking pan with cooking spray.
In a large mixing bowl, combine cake mix, eggs, water, vegetable oil, and vanilla. Beat with an electric mixer until smooth and mixed well. Pour batter into a prepared pan, smooth the top and bake for 22-24 minutes.
Let the cake cool for at least 30 minutes, then poke holes all over the cake with a bamboo skewer.
In a large bowl, combine evaporated milk, sweetened condensed milk, and half and half. Slowly pour over the cake, making sure to get in all the holes.
Top cake with plastic wrap and refrigerate for at least 3 hours.
Before serving, make the whipped topping by whipping cream with sugar and vanilla in a large bowl with an electric mixer or with a stand mixer. Mix until soft peaks form, then spoon and spread over the cake.