Melt the butter in a small frying pan over low heat. Add the hibiscus petals and cook for 5 minutes, then remove from heat and allow the petals to steep in the butter for 30 minutes, stirring every 5 minutes to help the petals release their color.
Puree the mixture in a blender or food processor, then place it in a small bowl and allow it to rest at room temperature until it solidifies (to speed this up you can place it in the refrigerator for 30 minutes, stirring it every 10 minutes to keep it cooling down evenly throughout.)
In the bowl of an electric stand mixer fitted with a paddle attachment, beat together the cream cheese and hibiscus butter at medium speed until completely smooth. Reduce speed to low and add the powdered sugar and vanilla extract, mixing until combined and then raising the speed to medium. Beat the mixture until smooth, light, and fluffy, about 5 minutes more.
For the rhubarb jam, bring the rhubarb, sugar, and water to a boil in a small saucepan over medium high heat. Reduce heat to low and continue cooking until the mixture turns jammy and the rhubarb disintegrates, about 15 minutes, stirring every few minutes. Remove from heat and set aside to cool to room temperature.
Preheat the oven to 350 degrees Fahrenheit. Grease 3 (8-inch) cake pans and line the bottoms with parchment paper and set them aside.
Stir together the flour, baking soda, baking powder, ginger, and cardamom in a medium bowl and set it aside.
Beat together the sugar and eggs in the bowl of an electric stand mixer fitted with the paddle attachment at medium speed until pale yellow and silky. Add the creme fraiche, olive oil, lemon juice, lemon zest, and vanilla extract and mix at low speed until combined. Add the flour mixture in two increments, mixing until just combined.
Evenly distribute the batter between the three pans, spreading it with a spatula so that it touches the interior edges of each pan. Place them in the oven and bake until lightly golden on top and a toothpick inserted into the center of each comes out clean, about 15 to 20 minutes.
Remove from the oven and allow to cool for 20 minutes before removing the cakes from the pans and allowing them to cool completely on a wire rack.
Spread the jam between each cake layer, then frost the outside of the cake with the hibiscus cream cheese buttercream and serve.