Preheat oven to 350 F. Grease and line an 8-inch cake pan with parchment paper on the bottom. Cut strips of parchment paper to line the sides of the pan. Parchment strips should be 2-3 inches taller than the cake pan in order to give the cake space to rise.
Separate the egg yolks and whites, placing the yolks in the bowl of a stand mixer with a whisk attachment, or in a large bowl. Beat the egg yolks, vanilla extract, and half the sugar on high speed for at least 5 minutes, until very pale and fluffy. Beatin the vanilla extract, milk, and vegetable oil.
Sift in the flour, and gently fold it in with a rubber spatula until just combined.
In a separate bowl, using a hand mixer, whip the egg whites on low speed. Slowly add the remaining sugar. Increase speed and whip for about 5-8 minutes until glossy and stiff peaks form.
Pour 1/4 of the egg white mixture into the egg yolk mixture and gently stir to losen it up. Add remaining egg whites to the egg yolk mixture in thirds, folding gently until just incorporated. Be sure to fold from the bottom of the bowl upwards, and around, as the thicker egg yolk mixture will have a tendency to get stuck there.
Pour the cake batter into the prepared pan. Bake for 60 minutes, until a toothpick inserted in comes out clean.
While the cake is baking, make the strawberry filling:
Combine the strawberries and sugar in a small saucepan and bring to a boil over medium heat. Continue cooking, stirring occasionally, until the strawberries dissolve and the mixture thickens. If the mixture is a watery, add 1 tbsp of cornstarch, diluted with 2 tbsp water to thicken. Let the strawberry filling cool to room temperature
Flip the sponge cake upside down and let it cool fully on a wire rack.
Once cooled wrap the sponge cake tightly in plastic wrap and allow to cool in the refrigerator or freezer until you are ready to assemble.