Lightly coat an 11 x 17-inch rimmed baking sheet with cooking spray; line the bottom with parchment paper, leaving a 1-inch overhang.
Spoon jam into a bowl, and beat with a rubber spatula to smooth out; set aside. In a large bowl, whisk flour, baking powder and salt to combine.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter, sugar and oil on medium speed until light and fluffy, 2 to 3 minutes. Scrape the bowl and the paddle. Add eggs one at a time, beating until smooth after each addition. Add vanilla. Scrape down again. With mixer on low speed, add the flour mixture in three batches, and beat until thoroughly combined.
Cover with plastic wrap and refrigerate for 30 - 60 minutes to firm up the dough.
Meanwhile, set the shelf to the middle, and preheat the oven to 350 degrees F.
Grate half of the dough into the prepared pan, gently evening it out so you don't see any holes. Spread the jam on top in an even layer. Grate the remaining dough evenly over the top.
Bake for 20 - 25 minutes until golden, rotating the sheet after 15 minutes. Cover loosely with foil if browning too quickly.
Cool for 5 minutes on a wire rack and then carefully lift the parchment and transfer to wire rack to cool completely. Transfer to a cutting board and cut into 2-inch squares. (7 x 5 rows)
Notes
If little pieces break off when grating the dough, gently form them into crumbles; they will all bake up together perfectly. Store between layers of parchment paper in an airtight container at room temperature up to 3 days. Freeze between layers of parchment paper in an airtight container.Adapted from The New International Goodwill Recipe Book, 6th Edition, 1981, Blanche Abrahams