Preheat your oven to 350°F (175°C). In a food processor, combine all-purpose flour, powdered sugar, and salt, pulsing until mixed. Gradually add cold, cubed butter and pulse until the mixture resembles coarse sand. Next, mix in the egg yolk, heavy cream, and vanilla extract, pulsing until it forms a soft dough. Press the dough evenly into a lined 9x9-inch baking dish, prick the surface with a fork, then freeze for about 15 minutes. Bake for 15 minutes with weights, remove weights, and bake for an additional 20 minutes until golden brown. Allow to cool completely.

In a small bowl, sprinkle unflavored gelatin powder over cold water and let it bloom for about 5 minutes. Meanwhile, in a double boiler, combine softened butter and granulated sugar, beating until creamy. Add the egg yolks, mango puree, salt, and fresh lemon juice, cooking over simmering water for 15-25 minutes until the mixture thickens and coats the back of a spoon. Remove from heat, stir in the bloomed gelatin until fully dissolved, then strain through a fine sieve to achieve a silky texture.

Once the shortbread crust has cooled completely, pour the mango curd over the crust, spreading it evenly. Carefully warm the raspberry jam in a small saucepan until just liquid, then dollop spoonfuls over the mango layer. Use a toothpick or skewer to gently swirl the raspberry jam into the curd, creating a beautiful marbled effect. Cover the dish with plastic wrap and refrigerate it for 4-6 hours, or overnight, until fully set.

After the bars have set, use a sharp knife heated under hot water for clean slicing. Cut the Raspberry Mango Bars into squares or rectangles and serve, showcasing their vibrant colors. For a delightful touch, dust with powdered sugar or add a fresh raspberry on top, enhancing the tropical flavor experience as you scoop up these delicious treats!