This traditional shortcake is a classic for a reason -- just about everyone loves the play of tart, juicy berries, airy whipped cream, and layers of delicate cake.
Heat oven to 350 degrees. Butter two 9-by-2-inch round cake pans; set aside. In a large bowl, sift together flour and cornstarch; set aside.
In the bowl of an electric mixer fitted with whisk attachment, combine eggs, egg yolks, granulated sugar, salt, and 1 teaspoon vanilla. Beat on high speed until mixture is thick and holds a ribbonlike trail on the surface when you raise the whisk, about 5 minutes.
Place reserved flour mixture on a large piece of parchment paper. Holding paper like a funnel, add flour mixture to egg mixture. With machine running on low speed, mix until just combined. In a steady stream, immediately add oil; mix until just combined. Remove bowl from mixer; detach the whisk. Using the whisk, fold mixture several times.
Divide batter between pans. Bake cakes, rotating pans halfway through baking time, until the centers spring back when you touch them with your finger, about 30 minutes.
Immediately turn cakes out onto a wire rack; let stand until completely cool.
Combine cream, confectioners' sugar, and remaining teaspoon vanilla extract in clean mixer bowl. Scrape in vanilla seeds; reserve pod for another use. Starting on low speed and increasing to medium high, whip until stiff peaks form, about 2 minutes.
Using a serrated knife, slice cakes in half; place one layer on a serving plate. Spread one-fourth of whipped cream over the layer; arrange strawberries on top. Repeat process with remaining layers, cream, and berries. Refrigerate until serving; garnish with mint.
This cake is best when assembled six to eight hours ahead; arrange the top layer of fruit just before serving.