Preheat the oven to 180°C or 350°F. In a bowl, beat the egg whites until stiff. Gradually add the sugar while continuing to beat. You should have a glossy mixture.
Reduce the mixer speed slightly and add the egg yolks, a pinch of salt, and the vanilla extract, mix well.
Then, turn off the mixer and use a spoon or spatula to fold in the sifted flour. Gently fold in the flour mixture until well combined.
Pour the cake mixture into a round pan (about 20 cm or 8 inches) lined with parchment paper and smooth it out with a spatula. Bake for about 25 minutes at 180°C or 30 minutes at 350°F, or until a toothpick inserted comes out clean.
For the meringue discs (2):
In a heatproof bowl, add the egg whites and sugar. Place the bowl in a double boiler over low heat. Be sure to stir constantly until all the sugar has dissolved. While the mixture is still hot, but removed from the heat, beat at full speed with an electric mixer until you have a stiff, glossy meringue. If desired, add cream of tartar or a few drops of lemon juice during the last few minutes. You can also add 1 teaspoon of cornstarch. This helps improve the consistency of the meringue.
Using a piping bag, form two meringue discs on a baking sheet or pan lined with parchment paper. Use a spatula to even them out and make sure they are the same size as the cake mold (20 cm or 8 inches). Bake the meringue discs on very low heat (100°C or 210°F) for 90 minutes, or until dry to the touch. If you have time, it's best to let them rest in the oven for 3-4 hours. Once the meringues are cold, remove the baking paper and place them on a plate.
To assemble the cake:
Carefully slice the sponge cake in half to create two layers.
Whip the cold heavy cream with the sugar and the vanilla extract until stiff peaks form and place it in a piping bag.
Cut the peaches into thin slices.
Microwave the dulce de leche for 30 seconds to make it easier to spread out.
Place the first cake layer on the serving plate and drizzle 1/3 cup of the syrup from the can of peaches over it.
Add a generous layer of dulce de leche and spread it evenly with a kitchen spatula.
Place the first meringue disc on top of the dulce de leche layer.
Add a generous layer of whipped cream using the piping bag. Next, arrange the peach slices on top of the cream layer so that they are evenly distributed and each cake slice will contain some of the fruit when you cut and serve the Chaja cake.
Place the second layer of sponge cake on top and repeat the steps listed below (add the peach syrup, the dulce de leche, and the meringue disc)
Decorate the outside and top of the cake with the remaining whipped cream and peach slices.
Let the cake rest in the refrigerator for a couple of hours before serving and enjoy!