Preheat your oven to 350°F (175°C). Grease and line a rectangular baking pan with parchment paper.
In a large bowl, beat the egg whites using an electric mixer on medium speed until frothy. Add cream of tartar and continue beating until soft peaks form.
Gradually add half of the granulated sugar to the egg whites, beating continuously until stiff peaks form. Set aside.
In another bowl, beat the egg yolks until light and creamy. Add the remaining granulated sugar and vanilla extract. Mix until well combined.
Slowly add the sifted flour into the egg yolk mixture, stirring until smooth.
Gently fold in one-third of the beaten egg whites into the egg yolk mixture to lighten it. Then, fold in the remaining beaten egg whites in two batches, being careful not to overmix.
Pour the batter into the prepared baking pan, spreading it evenly with a spatula. Bake for about 20 minutes or until the meringue is lightly golden.
While the meringue is baking, prepare the custard filling. In a saucepan, heat the sweetened condensed milk over medium-low heat until thickened, stirring constantly. Remove from heat and let it cool.
Once the meringue has cooled down, carefully transfer it onto a clean surface lined with parchment paper.
Spread the cooled custard filling evenly over the meringue, leaving a small border around the edges.
Starting from one end, carefully roll the meringue into a log shape, using the parchment paper to help you.
Sprinkle powdered sugar on top of the rolled meringue for a finishing touch.
Chill the Brazo de Mercedes in the refrigerator for at least 1 hour before serving. Slice, serve, and enjoy!