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Place a rack in center of oven; preheat to 325°. Using your fingertips, grease bottom and sides of a 9" round cake pan with vegetable oil. Line bottom of pan with parchment paper, smoothing to eliminate air bubbles. (It may sound fancy, but making a parchment circle is easy! Place pan on a piece of parchment, trace circumference with a pencil, then cut it out.)
Whisk 1⅓ cups all-purpose flour, 1¼ cups granulated sugar, 1¾ tsp. baking powder, ¼ tsp. baking soda, and 1¼ tsp. kosher salt in a large bowl. Sift ½ cup cocoa powder into bowl, then whisk to combine. (You can stop here and package these dry ingredients in an airtight container to create a sort of DIY cake mix if you want!)
Whisk 2 large eggs, ¾ cup vegetable oil, and 1 tsp. vanilla extract in a medium bowl until well combined and creamy, about 30 seconds. Using a spatula, mix egg mixture into dry ingredients until fully incorporated. It will be thick and pasty, that’s okay!
Warm 1 cup milk in a small saucepan over medium heat until it comes to just a bare simmer—make sure it doesn’t come to a boil. Whisk warmed milk into batter until lump-free and just combined; do not overmix.
Immediately transfer batter to prepared pan. Tap pan a few times on work surface to encourage some of the bubbles to escape.
Bake cake, turning pan halfway through, until a cake tester (or toothpick!) inserted into the center of cake comes out clean, 40–50 minutes. Transfer to a wire rack and let cake cool in pan.
Meanwhile, make the frosting: Fill a medium pot with 1" water and bring to a bare simmer over medium heat. Combine 4 oz. chocolate chips and ½ cup heavy cream in a heatproof medium bowl, place over saucepan, and reduce heat to low (make sure bottom of bowl is not touching water). Stir occasionally with a spatula until chocolate is melted and mixture is homogeneous and thick. Chill ganache until cool to the touch, about 25 minutes (you can mix with a spatula to encourage cooling). Alternately, mix chocolate and cream in a microwave-safe bowl and microwave in 10-second bursts until melted.
Using an electric mixer on medium-high speed, whisk 4 oz. (room temperature!) cream cheese, ¼ cup powdered sugar, and remaining ¾ tsp. vanilla extract and ¼ tsp. kosher salt in a large bowl until very smooth and no lumps remain. Beat in cooled chocolate ganache on medium speed, scraping down sides of bowl as needed, until frosting just holds its peak and is well combined and a little thicker, about 1 minute. You don’t want to overbeat because the frosting can become too stiff.
Run a butter knife around edges of pan. Invert cooled cake onto a plate and peel off parchment. Invert again onto a platter.
Top cake with frosting, spreading evenly across the surface. Make some decorative swooshes with a spoon, if desired. Slice and serve.