Step 1In a medium bowl, sift together the flour, the baking powder and salt and set the combined dry ingredients aside.
Step 2In the bowl of a mixer, beat the eggs with 1 cup sugar, oil and the vanilla (or cognac). With the mixer running, add the dry ingredients slowly. Continue to mix on medium-low speed until a smooth, shiny, uniform dough is formed that leaves the sides of the bowl but is still somewhat sticky. (Note: The consistency is right when it is easily removed from the mixer attachment. Add another tablespoon or two of flour, if necessary, but do not be tempted to add too much or the finished cookies will be hard).
Step 3Form the dough into a thick rectangle, wrap with parchment paper or plastic wrap, and chill until firm, 1 to 2 hours.
Step 4Heat the oven to 375 degrees. Line 2 cookie sheets with parchment paper and lightly grease the parchment with oil.
Step 5Place another piece of parchment paper on a work surface and sprinkle lightly with flour. Remove the dough from the refrigerator, and divide in half. Transfer half to the parchment paper, lightly flour a rolling pin and roll out the dough to form an approximate 12-by-16-inch rectangle, slightly more than one-eighth-inch thick. The dough will be somewhat moist. Cut and paste pieces of dough if necessary to form the rectangle.
Step 6In a small bowl, mix together the remaining 2 tablespoons sugar, cinnamon and finely chopped nuts. Use a spoon to make a thin strip of half the jam along one of the long sides of the rectangle, about 1 inch away from the edge. Sprinkle the remaining dough with half of the cinnamon-sugar-nut mixture, leaving a 1-inch margin from the sides.
Step 7Roll up from the long side jelly-roll style (so the jam is in the center), tuck under the edges and place on the diagonal on the prepared cookie sheet. Repeat with the remaining dough using a separate cookie sheet.
Step 8Bake until lightly browned, 30 to 35 minutes. Cool for 10 to 15 minutes, then carefully slice crosswise into three-fourth-inch thick slices using a serrated knife. Store in a covered cookie jar or freeze for up to 3 weeks. The cookies may also be frozen.