In medium saucepot over medium-high heat, add guava paste and ¾ cup water. Cook, stirring occasionally, until guava paste is smooth and thick, about 8 minutes; set aside to cool (you should have about 2 ¼ cups).
Meanwhile, add 1/3 cup sugar and 1/3 cup water to small saucepan over medium-high heat. Bring mixture to boil, stirring occasionally until sugar dissolves, transfer to small bowl. Stir in vanilla; set aside to cool.
Heat oven to 425°F. In medium mixing bowl, using electric mixer, beat egg whites until stiff (peaks of egg whites will not droop, and egg whites will not move when bowl is tilted); set aside. In medium bowl, whisk together egg yolks, remaining 2/3 cup sugar and salt until yolks are pale yellow. Mix in flour until combined. Using spatula, stir 1/3 egg whites into egg yolk mixture until combined. Gently fold in remaining egg whites until combined (mixture should be light and fluffy). Evenly spread mixture evenly in 11”x16” baking sheet lined with parchment paper. Bake until cake is light golden brown and springs back when gently pressed with finger, 10-15 minutes.
Invert cake onto kitchen towel or parchment paper dusted with confectioners’ sugar. Peel off top parchment layer; discard. Trim any ragged edges with knife. Using pastry brush, brush reserved vanilla mixture onto cake until absorbed. Starting with long side of cake, rolljellyroll style, into towel. Let sit, seam-side down, until cool.
Gently unroll cake. Using spatula, spread reserved guava filling evenly on surface of cake, leaving 1” borders all around. Reserve 1 tbsp. guava filling. Starting with long side, gently and firmly re-roll cake jellyroll style. Place cake seam side-down on serving platter. Brush thin layer guava mixture over outside of cake; chill until ready to serve. Dust with confectioners’ sugar before serving.