Prep: Preheat the oven to 350°F. Line the bottom of a 9x13" pan with parchment paper and set aside.
Steep the tea: Pour hot water over 3 of the jasmine tea bags. Cover and steep for 10 minutes. Set aside to cool until needed.
Flour mixture: In a small bowl, add the flour and baking powder. Cut open the remaining 2 jasmine tea bags and add the tea leaves. Stir together and set aside.
Separate the eggs: Separate the egg whites and egg yolks into two separate large mixing bowls, being careful not to get any of the egg yolks in the egg whites. Set the egg yolks aside.
Egg white meringue: To the egg whites, add the cream of tartar. Use an electric hand mixer to beat the egg whites on low-medium speed until it becomes frothy like cappuccino foam.
Whip to stiff peaks: Sprinkle in 100g of granulated sugar, one spoonful at a time, mixing well in between each addition. After all the sugar has been added, continue mixing on medium speed until it becomes stiff peaks. Set aside.
Egg yolk mixture: To the egg yolks, add the remaining 50g of sugar and mix briefly with the same hand mixer until the eggs are loosened. Add 70g of the cooled jasmine tea, oil, and vanilla extract. Mix to combine.
Sift in flour: Use a fine mesh sieve to sift in the flour mixture. Mix again until combined.
Combine meringue and egg yolk mixture: Add about ⅓ of the egg white meringue to the egg yolk mixture. Use a spatula to fold them together until mostly combined. Add the rest of the meringue and fold together until no streaks remain.
Fill pan: Pour the cake batter into your lined pan. Use an offset spatula to spread the batter into the corners and sides of the pan.
Bake: Bake for about 25-27 minutes or until the edges of the cake are lightly browned and the surface of the cake is just beginning to brown. Let the cake cool completely in the pan on a wire rack. Once cooled, run an offset spatula around the edges of the cake and invert the pan to release the cake sheet.
Cut out cake rounds: Use a 6" cake ring to cut out 3 cake layers. For the last cake round, cut the cake out in 3-4 pieces from the leftover edges of the cake sheet and arrange them together into a circle. With the scraps, you can either eat them as a snack or save them to make a cake box.