People will be so impressed with the fact that you made homemade baklava, and it is SO delicious! This uses a lot of nuts, and you can often find them at very affordable prices at a Middle Eastern or Mediterranean grocery.
Chop all the nuts (about a quarter to a sixth of a whole pistachio is a good guideline for size). In a bowl, combine the nuts, the seeds, and sugar.
Preheat oven to 300
Brush 8" square pan with butter.
Keep all filo sheets that are not being used properly covered with a piece of plastic wrap and then a damp towel. Remove one sheet at a time and work quickly.
Spread the first sheet in front of you on a clean, dry surface and brush generously with butter. Lay this sheet in the cake pan. The sheet will over flow on two sides. Fold the short side over first and brush with butter. Fold the longer side over and brush with butter, the whole sheet. Repeat with two more sheets. After you have buttered the third sheet, sprinkle about 2 1/2 tablespoons of the nut-seed mixture, evenly over the top. Lay another sheet over the nuts. Fold and butter as before. Put another layer of nuts and seeds. Alternate a sheet of pastry and a layer of nuts three more times. Top the final layer of nuts with three more buttered sheets. Butter the top generously.
If there is any butter left at this point, you can pour it over the top. Using a sharp knife, cut the baklava to form five even rows. Cut again on the diagonal to form diamonds. Bake at 300 for 1/2 hour and at 350 for another 1/2 hour.
Let baklava cool.
Mix syrup ingredients with 1.5 cups water. Bring to simmer over medium heat, turn heat very low and simmer uncovered for 8-10 minutes. Pour the hot syrup over the hot baklava, making sure it seeps through to the bottom of the pan. Cool and eat.