1. Prepare the Sponge Cake:

• Preheat and Prep Pan: Preheat oven to 350°F (175°C). Grease a 10×15-inch jelly roll pan. Line the pan with parchment paper, ensuring the parchment extends slightly up the sides. Grease the parchment paper as well.
• Beat Egg Yolks: In a large bowl, beat the egg yolks with 1/2 cup of the granulated sugar using an electric mixer until the mixture is pale yellow, thick, and ribbons form when the beaters are lifted (about 3-5 minutes). Beat in the vanilla extract and yellow food coloring (if using).
• Combine Dry Ingredients: In a separate medium bowl, whisk together the sifted cake flour, salt, and baking powder. Gently fold in the chopped dried mango.
• Whip Egg Whites: In another clean, grease-free bowl, using clean beaters, whip the egg whites on medium speed until soft peaks form. Gradually add the remaining 1/4 cup of granulated sugar, beating on high speed until stiff, glossy peaks form. Do not overwhip.
• Fold Batter: Gently fold about one-third of the whipped egg whites into the egg yolk mixture to lighten it. Then, gently fold in the remaining egg whites in two more additions, alternating with folding in the dry ingredients (flour/mango mixture). Fold until just combined; do not deflate the egg whites.
• Spread Batter: Pour the batter into the prepared jelly roll pan, spreading it gently and evenly with an offset spatula.
• Bake: Bake for 12-15 minutes, or until the cake springs back when lightly touched in the center.
• Prepare for Rolling: While the cake bakes, lay a clean kitchen towel flat on a work surface and dust it generously with powdered sugar.
• Roll the Cake: As soon as the cake comes out of the oven, immediately invert it onto the prepared, powdered sugar-dusted towel. Carefully peel off the parchment paper. Starting from one of the short ends, tightly roll the warm cake and the towel together into a spiral.
• Cool Rolled Cake: Let the cake cool completely in the rolled towel on a wire rack.

2. Make the Cheesecake Filling:

• In a medium bowl, beat the softened cream cheese, powdered sugar, and vanilla extract with an electric mixer until smooth and creamy.
• In a separate, chilled bowl, whip the very cold heavy cream with clean beaters until stiff peaks form.  
• Gently fold the whipped cream into the cream cheese mixture until just combined.

3. Make the Mango Topping:

• In a medium saucepan, combine the diced mango, granulated sugar, and lemon juice. Cook over medium heat, stirring occasionally, until the mango softens slightly, about 5-7 minutes.
• In a small bowl, whisk together the 1 tablespoon of cold water and the cornstarch until smooth (slurry).
• Stir the cornstarch slurry into the mango mixture in the saucepan. Cook for another 1-2 minutes, stirring constantly, until the sauce thickens.
• Remove from heat and let the mango topping cool completely.

4. Assemble the Cake:

• Unroll and Fill: Once the cake is completely cool, gently unroll it, leaving it flat on the kitchen towel. Spread the cheesecake filling evenly over the surface of the cake, leaving a small border along the edges.
• Re-roll: Carefully re-roll the cake without the towel.
• Chill: Wrap the rolled cake tightly in plastic wrap and refrigerate for at least 1 hour (or up to 4 hours) to allow the filling to set and firm up.

5. Decorate and Serve:

• Unwrap the chilled cake roll and place it seam-side down on a serving platter.
• Spoon the cooled mango topping evenly over the top of the cake roll.
• Garnish with extra diced mango or mango slices, if desired.
• Slice the cake roll with a sharp, serrated knife and serve chilled.