Preheat your oven to 350°F (175°C) and line an 8x8 inch baking dish with parchment paper. In a mixing bowl, blend together all-purpose flour, powdered sugar, and salt. Add cold, cubed butter and mix until crumbly. Incorporate the egg yolk, heavy cream, and vanilla extract until combined. Press this mixture firmly into the prepared pan, pricking the surface with a fork. Freeze for 20-30 minutes before baking.

Once the crust has chilled, bake it in the preheated oven for 15 minutes using pie weights or foil for support, then remove weights and bake for an additional 20 minutes until golden brown. The edges should be slightly crisp, while the center remains firm. Remove the crust from the oven and allow it to cool completely in the pan before adding the mango curd.

In a small bowl, bloom the unflavored gelatin powder in cold water for about 5 minutes. Meanwhile, in a double boiler, combine softened butter and granulated sugar, stirring until melted. Add the egg yolks, mango puree, and fresh lemon juice, whisking continuously until thickened, about 8-10 minutes. Once warm, stir in the bloomed gelatin until fully dissolved and smooth, then strain the mixture to eliminate any solids.

Pour the silky mango curd over the cooled shortbread crust, spreading it evenly to create a smooth layer. This curd will form the luscious filling for your Raspberry Mango Bars. Allow this to set for a few minutes at room temperature while you prepare the raspberry swirl.

Warm the raspberry jam in a small saucepan over low heat until it becomes slightly pourable, about 1-2 minutes. Drop spoonfuls of the warm jam onto the mango curd, then use a knife or skewer to gently swirl the jam into the curd, creating beautiful patterns. Avoid over-mixing; you want to keep those vibrant raspberry swirls visible!

Refrigerate the assembled Raspberry Mango Bars for at least 4-6 hours, or until set completely. This step is essential for achieving clean slices when you cut the bars. The curd should be firm to the touch, with the vibrant swirls holding their shape.

Once chilled and set, carefully lift the bars out of the pan using the edges of the parchment paper. Slice into squares with a warmed knife for clean edges. These delightful Raspberry Mango Bars are now ready to be shared and enjoyed, perfect for any occasion!