Preheat oven to 350°F (175°C) and position rack in center. Butter two 8-inch or 9-inch round cake pans, line bottoms with parchment paper, butter parchment, dust sides with flour, and tap out excess.
In a medium bowl, whisk together the all-purpose flour, baking powder, and fine salt until well combined. Set aside.
Place chopped semisweet chocolate in a small microwave-safe bowl and microwave in 20-second intervals, stirring between each, until completely smooth (60-90 seconds). Add cocoa powder and whole milk, then stir vigorously until fully combined. Set aside to cool slightly.
In a stand mixer fitted with the paddle attachment, beat softened butter, vegetable oil, and granulated sugar on medium speed for 4-5 minutes until very light, pale, and fluffy. Scrape down sides as needed.
With mixer on low, add eggs one at a time, letting each fully incorporate before adding the next. Add vanilla extract and mix 30 seconds on medium speed. Scrape down bowl well.
Reduce mixer speed to low. Add one third of flour mixture and mix until barely combined. Pour in half the buttermilk and mix gently. Add another third of flour, mix briefly, then add remaining buttermilk. Finish with remaining flour and mix only until no flour streaks remain. Fold gently by hand with a rubber spatula to ensure even mixing, being careful not to overmix.
Scoop approximately one third of the vanilla batter (about 2 cups or 480ml) into the bowl with cooled chocolate mixture. Fold gently but thoroughly until no vanilla streaks remain and the chocolate batter is smooth.
Using a large spoon or ice cream scoop, alternate dropping large spoonfuls of vanilla and chocolate batter into each prepared pan. Insert a butter knife about halfway down and use a gentle figure-eight motion to swirl 2-4 times, being careful not to over-swirl.
Place both pans on the center rack and bake for 28-35 minutes, or until a toothpick inserted in the center comes out clean with just a few moist crumbs. Avoid opening the oven door during the first 25 minutes.
Remove from oven and cool in pans on a wire rack for 15 minutes. Run a thin knife around the edges, invert onto the wire rack, peel off parchment paper, then flip cakes right-side up. Cool completely (at least 1-2 hours) before adding ganache.
Place semisweet chocolate chips in a medium heat-proof bowl. Heat heavy cream in a small saucepan over medium heat until just simmering around the edges (do not boil). Pour hot cream over chocolate chips, let sit for 2 minutes, then whisk gently from the center outward until silky and smooth. Let cool for 5-10 minutes until slightly thickened.
Place one cooled cake layer on a serving plate. Pour or spread a thin layer of ganache over the top. Place the second cake layer on top and pour remaining ganache over the top, using an offset spatula to guide it toward the edges and let it drip naturally down the sides. Let ganache set for at least 20 minutes before slicing.