Place nuts in the food processor and pulse until finely chopped but not powdery. Add the sugar and ground spices and pulse a couple more times to mix.
Brush the bottom and sides of a 12 X 9 inch baking pan with vegan butter or olive oil. Carefully layer one filo pastry sheet in the bottom of the baking pan and brush it with butter. Continue layering and brushing with vegan butter or oil until you've used up a third of the sheets. (A package of filo pastry typically yields 21 9' X 24' sheets, so you will have around 14 half-sheets in each layer.)
Layer half the nuts over the final layer of filo. Continue layering another 14 sheets, brushing each layer with butter. Sprinkle the remaining nuts over the top in an even layer.
Layer on the final third of filo sheets, brushing each with vegan butter or oil. Use a sharp knife to carefully cut diamond shapes in the layered baklava, cutting all the way to the bottom. Bake in a preheated 400-degree oven for 50 minutes.
About 25 minutes before the baklava is done, place the ingredients for the sugar syrup in a saucepan and bring to a boil. Once the syrup boils lower heat to a simmer and let it cook 20 minutes.
As soon as the baklava comes out of the oven pour the hot sugar syrup evenly over it. If you hand-pound the spices, as I did, you can use a strainer to strain them out--they've already added all their flavor to the syrup.
After pouring the syrup over the baklava, you can optionally top it with more nuts and rose petals for a pretty look. Let the baklava cool to room temperature, then run the knife once more along the cuts you made earlier and remove each piece carefully.
Immediately after pouring the syrup over the baklava, you can optionally top it with more nuts and rose petals for a pretty look.