Step 1: Preheat your oven to 350°F (175°C). Line a 10×15 inch jelly roll pan with parchment paper, leaving an inch of overhang on the sides.
Step 2: In a large bowl, whisk the 4 egg yolks with 1/2 cup of granulated sugar and vanilla extract until the mixture is pale yellow and thick.
Step 3: In a separate clean bowl, beat the egg whites until soft peaks form. Gradually add the remaining 1/4 cup of sugar and continue beating until stiff, glossy peaks form.
Step 4: Sift the cake flour, baking powder, and salt into the yolk mixture. Add the oil and milk, and stir until just combined.
Step 5: Gently fold the egg whites into the batter in three additions using a spatula, being careful not to deflate the air bubbles. Pour the batter into the prepared pan and smooth the top.
Step 6: Bake for 10-12 minutes or until the cake is lightly golden and springs back when touched. Immediately flip the hot cake onto a clean kitchen towel dusted with powdered sugar. Remove the parchment and roll the cake up with the towel from the short end. Let cool completely.
Step 7: Whip the heavy cream and powdered sugar until stiff peaks form. Unroll the cooled cake, spread the cream evenly, and sprinkle with chopped strawberries. Roll the cake back up tightly, wrap in plastic, and refrigerate for 2 hours before slicing.