Preheat your oven to 350°F. Grease a 9x13-inch baking pan or line it with parchment paper.
In a large bowl, whisk together the flour, sugar, baking soda, baking powder, and salt.
In another large bowl or the bowl of a stand mixer, use an electric mixer to cream the softened butter until light and fluffy. Add the oil and mix until smooth.
Beat in the vanilla, whole egg, and egg yolks until fully combined.
Gradually mix half of the dry ingredients into the wet ingredients. Then, mix in the milk. Finally mix in the rest of the dry ingredients mixing until just combined. Don’t overmix.
Pour the batter into the prepared 9x13 pan and smooth the top. Bake for 35–40 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool completely in the pan.
Make the Frosting, In a large bowl or bowl of a stand mixer, beat the softened butter until creamy. Sift in the powdered sugar and cocoa powder. Mix on low until mostly incorporated, then add the cream and salt. Beat on high for 2–3 minutes until light and fluffy. Add more cream if needed.
Once the cake is completely cool, spread the frosting evenly over the top. Add sprinkles, chocolate shavings, or keep it simple—your call!