Preheat oven to 350 degrees. Butter and line a rimmed 15-by-10-by-1-inch jelly roll pan with parchment paper; set aside.
In a large bowl, beat egg yolks and sugar together until light in color, about 1 minute; stir in 1/2 teaspoon vanilla. Add cake flour and baking powder; stir until well combined.
In the bowl of an electric mixer fitted with the whisk attachment, beat egg whites until stiff peaks form. Gently fold into flour mixture.
Pour cake batter in prepared pan and spread evenly with a spatula or the back of a spoon. Transfer baking sheet to oven and bake until cake springs back when touched, about 20 minutes.
Meanwhile, set 6 strawberries aside for garnish. Thinly slice remaining strawberries. Place heavy cream in the bowl of an electric mixer fitted with the paddle attachment; beat on medium speed. Slowly add remaining teaspoon vanilla and 2 tablespoons confectioners' sugar. Continue beating until soft peaks form. Set half of the whipped cream aside. Gently fold sliced strawberries into remaining half; set aside.
Lay a clean kitchen towel flat on a work surface with one of the short ends facing you. Generously sprinkle dish towel with confectioners' sugar. Flip cake onto towel, remove baking sheet, and peel off parchment paper. Using the dish towel, roll cake away from you; let cool.
Unroll cake. Evenly spread strawberry whipped-cream mixture over surface of the cake and re-roll. Transfer cake to a serving plate and evenly spread top and sides of cake with reserved whipped cream. Cut reserved whole strawberries in half lengthwise and place on top of cake for garnish.