Preheat the oven to 350°F (176°C). Coat three 9-inch round cake pans with vegetable shortening, line the bottoms of the pans with parchment paper, and spray with nonstick cooking spray.
In a large bowl, whisk together the flour, baking powder, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter until light and fluffy. Add the sugar on low speed and beat until smooth, about 3 minutes. Add the eggs and egg yolks, 1 at a time, beating until blended and scraping the bowl as necessary.
Reduce the mixer speed to low. Add the cream, evaporated milk, and vanilla and beat until smooth. Add the flour mixture and beat until blended. Increase the mixer speed to high and beat until smooth, about 1 minute.
Divide the batter equally among the prepared pans. Bake until a toothpick inserted into the center comes out clean, 30 to 35 minutes. Let the cakes cool in the pans for 10 minutes before turning them out onto wire racks to cool completely. Remove the parchment paper.