Before doing anything else, make sure that you have thawed your phyllo dough according to package instructions.
Start by making your syrup so that it has time to cool while the vegan baklava bakes. Add all of the ingredients to a small saucepan. Bring it to a boil and then immediately reduce it to a steady simmer. Cook for 15-20 minutes, or until reduced in volume and thick enough to coat the back of a spoon. Remove from the heat and set aside to cool. Remove the cinnamon stick and cloves if used.
Meanwhile, make the filling. Pulse the pistachios and walnuts in a food processor until crumbs are formed.
Add the cinnamon, lemon zest, and orange zest, ground cloves, nutmeg, and salt if using. Stir, then add the maple syrup and stir again to combine everything.
Preheat the oven to 350 degrees Fahrenheit. Lightly grease an 8-by-8-inch baking dish, or similar sized dish.
Open your phyllo dough. If you are buying a usual 16-oz box, it will have two rolls of dough inside, and you only need one of them. Gently unroll the dough, and trim it to the size needed to fit your pan. For my 8-by-8 pan, I sized it by cutting the entire stack of dough in half and then trimming a little bit off of one edge. Get a damp kitchen towel and use it to cover the dough to keep it moist.
Add approximately 3 sheets of dough at a time to your pan. Brush with a very light coating of olive oil and continue. Do this until you have used about 1/3 of the sheets.
Sprinkle 1/2 of the spiced nut filling onto the dough. Gently spread it out into an even layer as best you can without tearing the dough too much.
Continue layering and oiling sheets of dough until you have used approximately 2/3 of the sheets. Add the remaining half of the filling at this point, and finally, continue with the remainder of the dough. After lightly brushing the top layer of dough with oil, use a sharp knife to cut the baklava into pieces of your choosing (I went with a diamond pattern as seen here). Be sure to cut all the way through to the bottom of the pan.
Bake uncovered for approximately 25-28 minutes, or until nicely browned on top. Immediately after removing the baked vegan baklava from the oven, pour the syrup evenly over it. Try to get some of it it in all of the different cuts so that it can soak through to the bottom.
Let cool to room temperature before slicing and serving. Leftovers can keep in an airtight container in the refrigerator for a few days, or frozen.
Notes
NUTS: You can mix and match pistachios, walnuts, and almonds in whatever ratios you prefer to reach about 2 cups total.SWEETENER SUBSTITUTES: You can substitute maple syrup for agave and vice versa, if desired. Agave is slightly sweeter so adjust the quantity slightly to accommodate.OLIVE OIL: This is best with light tasting olive oil, not grassy extra-virgin olive oil. If you only have super flavorful olive oil, use a 50-50 mixture of olive oil and a neutral vegetable oil like grapeseed, to tone down its flavor a little bit. You can also use melted vegan butter if you're into that sort of thing.