How to Make It
Make the Cake: Preheat oven to 350°F. Lightly butter a 9-by-13-inch baking pan and dust with flour, tapping out excess.
Whisk together flour, baking powder, salt, and baking soda in a medium bowl; set aside.
Using an electric mixer fitted with the whisk attachment, beat eggs and sugar on medium-high until pale and thick, about 4 minutes. With mixer running, add melted butter and oil and beat until evenly combined. Beat in vanilla extract.
With mixer on low, add flour mixture in 3 additions and milk in 2 additions, beginning and ending with flour mixture. Mix just until combined (do not overmix).
Transfer batter to prepared baking pan and bake until a toothpick inserted in center comes out clean, 35 to 40 minutes. Let cool completely.
Make the Frosting: Place both types of chocolate chips in a large bowl. Heat cream and salt in a medium saucepan over high. As soon as mixture begins to boil, pour over chocolate and let stand for 3 minutes. Add vanilla extract and whisk until melted and smooth. Let cool to room temperature, stirring occasionally.
Using an electric mixer, beat ganache until fluffy and a shade lighter, about 4 minutes. Spread evenly over cake.