Preheat the oven to 350°F (175°C). Line a 15x10-inch jelly roll pan with parchment paper and lightly grease it.
Beat eggs on high speed for 5 minutes until thick, pale, and tripled in volume. Gradually add sugar while beating until fully combined and fluffy.
In a separate bowl, whisk flour, salt, and baking powder. Gently fold the dry mix into the egg mixture using a spatula, keeping the batter light.
Fold in lemon juice, melted butter, and vanilla extract until smooth and well blended, without deflating the batter.
Pour batter into the prepared pan and spread evenly. Bake for 12–15 minutes until lightly golden and the cake springs back when pressed.
Turn the warm cake onto a towel dusted with powdered sugar. Peel off the parchment. Starting from a short side, roll the cake up with the towel and let it cool completely.
Whisk together 1 cup powdered sugar and 2 tablespoons lemon juice until smooth and pourable.
Unroll the cooled cake and spread lemon cream or lemon curd evenly across the surface. Roll it back up, this time without the towel.
Place the cake seam-side down on a serving plate. Drizzle with lemon glaze and sprinkle with fresh lemon zest.