1. Make the Cake: Preheat oven to 350 degrees F. Grease two 9-inch cake pans and line the bottoms with parchment paper. Grease the parchment, then dust the pans with flour, tapping out any excess; set aside.
2. In a large bowl, whisk together the flour, baking powder, baking soda, salt and 1½ cups of the sugar. In a 4-cup liquid measuring cup or medium bowl, whisk together the melted butter, buttermilk, vegetable oil, vanilla extract, and egg yolks.
3. Place the egg whites in the bowl of a stand mixer fitted with a whisk attachment. Beat the egg whites at medium-high speed until foamy, about 30 seconds. With the mixer running, gradually add the remaining ¼ cup of sugar; continue to beat until stiff peaks form, about 30 more seconds. Transfer to a bowl and set aside.
4. Add the flour mixture to the now-empty mixing bowl fitted with the whisk attachment. With the mixer running on low speed, gradually pour in the butter mixture and mix until almost incorporated (a few streaks of dry flour should remain), about 15 seconds. Scrape down the sides of the bowl, then beat on medium-low speed until smooth and fully incorporated, 10 to 15 more seconds.
5. Using a rubber spatula, stir one-third of the egg whites into the batter to lighten it. Then, add the remaining egg whites and gently fold them into the batter until no white streaks remain. Divide the batter evenly between the prepared cake pans. Lightly tape the pans against the counter 2 or 3 times to pop any air bubbles.
6. Bake until the cake layers begin to pull away from the sides of the pans and a toothpick inserted into the center comes out clean, 20 to 22 minutes. Cool the cakes in the pans on a wire rack for 10 minutes, then loosen the cakes from the sides of the pans with a small knife, then invert onto greased wire racks. Peel off the parchment, turn right-side-up and cool completely, about 1½ hours.
7. Assemble the Ice Cream Cake: Spray a 9×3-inch round cake pan (or springform/cheesecake pan) with nonstick cooking spray. Line the bottom of the pan with a round of parchment. Then cut two strips of parchment that are 3 inches wide by 14 inches long. Line the sides of the pan with the parchment strips, overlapping them slightly. Spray a bit of nonstick spray where the ends overlap to help them adhere.
8. If the cooled cake has a domed top, trim off the domed portion with a long serrated knife to achieve a level surface. Place one of the cake layers in the bottom of the prepared cake pan for the base of your ice cream cake. (There will likely be some space between the sides of the pan and the cake, so try centering the cake as best you can.)
9. If you are using homemade ice cream, churn the ice cream base according to your machine’s instructions and transfer it directly from the machine into the cake pan. If your ice cream has been stored in the freezer (or if you’re using store-bought), allow it to soften in the refrigerator for 20 to 30 minutes, until it’s slightly softened and spreadable. Use an offset spatula to nudge the ice cream all the way to the sides of the pan, filling any gaps or holes, including any space between the cake and the pan. Rap the filled cake pan sharply on the counter a few times to encourage any air bubbles to rise to the surface and smooth the top.
10. Place the second cake layer over the ice cream, centering it on top. Cover the pan with plastic wrap and put the assembled cake in the freezer and freeze overnight.
11. Make the Fudge Frosting: Combine the powdered sugar, evaporated milk, chocolate chips and butter in a medium saucepan over medium-high heat. Bring the mixture to a boil and cook for 8 minutes, stirring constantly. Remove from the heat and stir in the vanilla extract. Allow to cool for 30 minutes.
12. When ready, pour the chocolate topping evenly over the top cake layer, spreading with an offset spatula if necessary. Return to the freezer for at least 2 hours, or until firm.
13. To Serve: At least 1 hour (and no more than 12 hours) before serving, unmold the cake. To release the cake from the pan, invert the cake onto a plate or cardboard round the same size and wrap a hot kitchen towel around the cake pan, keeping it there for 30 seconds, or until the cake loosens, and slide the pan off. Remove the parchment (and bottom of pan if using a springform). Top with a serving plate and turn the cake right side up. Return to the freezer for at least 10 minutes.
14. Remove the cake from the freezer 5 minutes before serving to soften it slightly. A hot, dry knife will yield the cleanest cuts. Dip your knife in a glass of hot water, wipe it clean with a towel, and cut a slice. Repeat between every slice.