Linzer Crumble Pie with Cranberry-Raspberry Jam

Filling: In a large saucepan, bring cranberries, raspberries, sugar, and vanilla pod and seeds to a boil over high heat, stirring. Continue cooking, stirring occasionally, until fruit is soft, about 10 minutes total. Pass through a fine sieve, pressing on solids; discard solids. (You should have 3 cups.) Let cool completely. Filling can be stored in the refrigerator up to 1 week.

Crust: Preheat oven to 350 degrees. Coat a 17-by-12-inch rimmed baking sheet with cooking spray. Line with parchment, leaving overhang on 2 long sides. Spray parchment.

Beat 3 sticks butter with sugar on medium-high speed until light and fluffy, about 3 minutes. Reduce speed to low, add flour and salt, and beat until dough forms clumps but does not completely hold together. Mix in hazelnuts. Reserve 1 1/2 cups dough; press remaining dough into prepared baking sheet in an even layer. Rub remaining 1 tablespoon butter into reserved 1 1/2 cups dough until larger clumps form.

Spread filling evenly over bottom crust. Crumble remaining dough on top in a lattice pattern. Bake 30 minutes. Cover with foil and continue baking until jam is bubbling, about 15 minutes. Let cool completely in pan on a wire rack. Use a paring knife to release short sides of crust from pan, then use parchment to lift pie out of pan and onto a cutting board. Cut into squares or triangles to serve. Pie sections can be stored at room temperature up to 3 days.