Place rack in center of oven, and preheat oven to 325 degrees. Brush a 9-by-9-inch pan with melted butter. Set aside.
Combine almonds, walnuts, and cinnamon in a medium bowl. Set aside.
Place one sheet of phyllo on a flat work surface. Brush with melted butter. Fold the long sides in to form a 9 1/2-by-15-inch rectangle. Brush folded edges with butter. Place a second piece of phyllo over first sheet, and gather it like a curtain to fit inside rectangle. Brush with butter.
Sprinkle 3 tablespoons of the nut mixture over the bottom one-third of the phyllo rectangle. Fold phyllo over to cover nuts. Brush folded phyllo with butter. Spread 1/4 cup nuts in a 1-inch-wide line parallel to, and about 1 inch from, the edge of pastry. Fold over once to cover nuts. Roll like a cigar almost to the end. Fold in ragged edges, and brush them with butter. Finish rolling, and fold ends under. Place seam-side down in prepared pan. Brush with butter. Repeat with remaining phyllo and filling, laying each roll next to the other so they are touching. Cut rolls crosswise into 21 pieces total (drag knife through a second time to assure a clean cut).
Transfer to oven, and bake until crust and nuts are evenly golden, 1 hour to 1 hour and 15 minutes. Remove pan from oven, and cool for 10 minutes. Pour cool Honey Syrup over pastry; it will come about three-quarters of the way up the sides. Let sit until most of the liquid is absorbed and nuts are saturated, about 30 minutes.
Phyllo is tricky to work with: Once it's unwrapped, the tissue-thin layers must be kept from drying out. Lili suggests taking out only what you need, covering the rest with plastic wrap, and then wrapping a damp towel around the plastic. Even after the rolled baklava is sitting in the pan waiting to go in the oven, Lili brushes the dough lightly with melted butter to keep it moist.