Preheat oven to 350F. Butter bottom of two 8-inch round cake pans and line with parchment paper. Butter and flour the parchment paper and pan sides. In a medium bowl, whisk together flour, baking powder, and salt; set aside.
Beat butter and 1/2 cup sugar on high speed in a large bowl until light and fluffy. Add eggs and yolks, one at a time, beating well after each addition. Beat in vanilla. Switch mixer to low setting. Add 1/2 cup flour mixture, then 1/4 cup milk, 1 /2 cup flour, 1/4 cup milk, and finally the last 1/2 cup flour. Mix until just combined, do not overmix.
Divide batter between two prepared pans.
Bake until a toothpick inserted in center of cake comes out clean, about 13-15 minutes. Let cakes cool in pans for about 10 minutes and then invert onto wire racks to finish cooling.
Combine strawberries and 1/4 cup sugar in a large bowl. Set aside.
Beat cream, 1/4 cup powdered sugar, and pinch of salt with an electric mixer until soft peaks form.
Put one cake on serving platter and arrange half of strawberries on it.
Top with half of whipped cream, leaving about an inch border.
Gently place the second cake on top.
Top cake with remaining whipped cream, leaving a 1-inch border.
Just before serving, spoon the rest of the strawberries over cake.