Preheat oven to 350°. Grease bottom of a 13- x 9-inch baking dish. Beat first 4 ingredients with an electric mixer at low speed 30 seconds, then at medium speed 2 minutes, scraping bowl occasionally.
Pour batter into pan, and bake at 350° for 25 to 30 minutes or until edges are golden brown and a wooden pick inserted in center comes out clean. Cool cake in pan 15 minutes. Pierce top of cake multiple times using a small wooden pick.
Combine cream, condensed milk, and evaporated milk in a small bowl; gradually pour and spread over warm cake, about 1/4 cup at a time, allowing mixture to soak into cake before pouring more. Let stand 2 hours; cover and chill overnight.
Bring half-and-half to a boil. Pour into a medium bowl with chocolate chips, whisking constantly until mixture is smooth. Pour evenly over chilled cake.