Preheat the oven to 375 degrees F (190 degrees C). Grease and flour a 15x10x1-inch jelly roll pan.
Break eggs into a small mixing bowl; beat with an electric mixer until thick and lemon-colored. Beat in sugar gradually. Add water, lime zest, and vanilla extract and blend well. Beat in flour gradually until smooth. Pour into the prepared pan.
Bake in the preheated oven until golden brown, about 12 minutes. Remove from the oven and loosen the edges with a sharp knife. Turn out immediately onto a tea towel sprinkled with powdered sugar.
Cut guava paste into chunks and place in a microwave-safe bowl. Microwave in 20-second intervals, stirring in between, until spreadable. Be careful, it will get hot because of the high sugar content.
Trim any stiff edges off of the cake and spread guava over. Roll up carefully in jelly roll fashion from the narrow end, using the towel to ease the cake over. Let cool in the towel on a wire rack for about 30 minutes.
Remove the towel carefully and sprinkle additional powdered sugar over the top if desired. Slice to serve.