Preheat oven to 350 degrees. Line a 8 X 8″ baking pan with a foil or parchment.
In a medium mixing bowl, whisk together the flour, ⅓ c. granulated sugar, and salt. With a pastry blender cut in the 8 tbsp. of butter until the mixture resembles wet sand. Reserve half of the mixture for the topping
Sprinkle half of the mixture into the prepared pan and press into an even layer. Bake the crust until the edges begin to brown (15-17 minutes). Remove and allow to cool for 10 minutes.
Meanwhile, combine the reserved flour mixture, oats, nuts, and brown sugar together in a medium bowl. Add the remaining 2 tbsp. butter and mix until small clumps begin to form. Set aside.
In a small bowl using a rubber spatula, combine the jam, raspberries, sugar, cornstarch, vanilla, lemon juice and zest together.
Spread the berry mixture evenly over the warm crust, then sprinkle with the streusel topping. Place in oven and bake until the filling is bubbling and the topping is golden brown (24 to 26 minutes), rotating the pan halfway through baking.
Remove from oven and let the bars cool completely in the pan on a wire rack for about 1 hour. Remove the bars from the pan using the foil, cut into squares, and serve.