Preheat the oven to 350F. Butter a 13x9-inch baking pan or spray with baking spray.

In a large bowl, whisk together the flour, baking powder, and salt.

In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the eggs and sugar together on medium-high speed very pale, thick, and fluffy for about 2 minutes. Add the peanut butter, oil, and vanilla, and beat on medium-low speed until well combined.

With the mixer running on low speed, gradually add in the flour mixture alternating with the evaporated milk. Stop and scrape down the bowl and mix again to ensure the batter is evenly combined. Pour the batter into the cake pan.

Bake for 25 to 30 minutes or until a toothpick inserted into the center comes out clean. Let the cake cool until slightly warm, about 30 minutes. (The cake may shrink a touch as it cools.)

In a medium bowl, whisk together the condensed milk, evaporated milk, and cream until well combined. Poke the cake all over with a fork or skewer. Slowly pour 2½ cups of the syrup over the cake, reserving the rest of the syrup for serving. Cover and chill for at least 2 hours or up to 24 hours.

In a small microwave-safe bowl, combine ½ cup cream and the peanut butter. Microwave for 15 seconds, or just long enough to warm the mixture. Stir together until fluffy combined.

In a large mixing bowl, beat the remaining 1½ cups of cream and the powdered sugar on medium speed until soft peaks form. Spread over the cake. Dollop the peanut butter over the whipped cream and swirl together with an offset spatula or a spoon. The cake can be covered and refrigerated for 1 day before serving. Serve with a generous pour of the remaining syrup on a dessert plate before placing the slice of cake.