Preheat the oven to 375°F. Line a jellyroll pan with parchment paper. Set aside.
Prepare the filling: Place the pistachios, almonds, pecans, halvah, and vanilla into the bowl of a food processor fitted with the metal “S” blade. Pulse until ground but not a paste. Set aside.
Prepare the syrup: Place the sugar, honey, water, and lemon juice into a medium pot. Over medium heat, bring to just a boil. Turn down to a simmer; cook for 10 minutes. Set aside.
Place a sheet of phyllo lengthwise on the work surface. Brush with canola oil. Top with another layer of phyllo. Brush with canola. Top with a third layer of phyllo and oil. Roll all four edges ½-inch inward to make a frame. Brush rolled edges with oil.
Spread a thick layer of the nut filling over the phyllo. Starting with a short end, roll up, jellyroll fashion; transfer to prepared sheet. Repeat, making 4 more rolled logs. Brush the logs with oil. Using a serrated knife, cut 4 diagonal slits across the top of each log.
Bake, uncovered, for 12 minutes, or until golden. Remove from oven and immediately spoon the syrup over the logs. Slice each log into 4-5 slices. Serve 2 slices to a plate. Drizzle with more syrup around the plate.
Recipe posted with permission from Kosher By Design Brings It Home: picture-perfect food inspired by my travels, by Susie Fishbein