To make the syrup: In a medium saucepan over medium heat, combine all the ingredients, bring to a boil. Reduce the heat and simmer for 20 to 30 minutes. Set aside to cool, then strain into a medium bowl.
Preheat the oven to 300 degrees F.
To make the filling: In a clean bowl, add egg white and beat with a hand mixer until thick, about 5 to 6 minutes. In a medium bowl, combine the walnuts, pecans, brown sugar and cloves. Gently fold in the egg whites and 3/4 cup of the syrup, until combined.
To assemble: Remove the phyllo from the package, being careful to keep it covered and cool. Take out 1 sheet and put it on a work surface. Gently brush with butter and fold in half. Add approximately 1/4 cup filling, toward the bottom half of the pastry and fold over the long end. Roll up, tucking in the ends as you roll. Set on a parchment lined baking sheet and brush with butter. Repeat until all cigars are assembled. Bake in the preheated oven for 25 to 35 minutes, keeping an eye on them so they don't brown too quickly.
Remove from oven, let cool for 2 minutes. On a clean work surface, cut the baklava in half on the diagonal and transfer to a serving tray or platter. Drizzle with remaining syrup, sprinkle with slivered almonds and dust with powdered sugar. Can be served warm or at room temperature.