For the dough: In a large bowl, stir together flour, baking powder, cardamom, and salt. In the bowl of a stand mixer, cream together butter and sugar until fluffy. Add egg yolks and vanilla extract and mix until well combined. Gradually add in dry ingredients while mixer is on low, until combined. Will be crumbly.
Pack dough into two balls, one which is slightly smaller than the other. Wrap each ball separately in plastic wrap and freeze for at least an hour.
While the dough is in the freezer, prepare the filling. Combine rhubarb, strawberry jam, sugar, and water in a small saucepan over low heat. Cook, stirring frequently, until rhubarb is softened and breaks down. This should take about 10 to 15 minutes. Remove from heat and stir in vanilla. Place in a bowl to cool (you can stick it in the fridge if necessary).
Preheat oven to 350°F. Prepare a 10-inch springform pan by greasing or spraying it. Using a box grater, grate the larger ball of dough into the springform pan (using the largest holes). Pat down gently to form the bottom crust. Spread rhubarb filling over the bottom layer, leaving a border of about a half inch around the edge. Then grate the smaller ball of dough over the top. Pat down gently if necessary.
Bake until golden brown, about 30 minutes. Cool completely before slicing and serving.