Make the syrup first so it can cool while the baklava bakes. Combine all the syrup ingredients in a small saucepan and bring to a boil. Reduce heat and simmer for a few minutes. Remove from heat and allow to cool. When cool, strain into clean measuring cup with a spout on it.
In a bowl, combine the pistachios, sugar, coconut, and zest. Set aside.
Melt the stick of butter in a small pan. Using a pastry brush, sprinkle a bit of the butter onto the sheet pan. Lay the first sheet of phyllo on and sprinkle with a bit more butter. Continue layering until you’ve used 8 sheets of phyllo dough, sprinkling butter in between each sheet.
After the eighth sheet, sprinkle once again with butter and spread about a third of the pistachio filling mixture evenly over the phyllo.
Layer 3 more sheets of phyllo on top of filling, sprinkling butter in between each sheet. Spread half of the remaining pistachio mixture on top and then layer 3 more sheets of phyllo, sprinkling butter between each sheet. Spread remaining pistachio mixture on, then layer about 8 more sheets of phyllo on top, sprinkling with butter between each sheet. Sprinkle some butter on the very top layer and using a sharp knife, score the baklava into diamond shapes.
Bake the baklava for approximately 55 minutes to an hour, checking on it at about 45 minutes. It should be golden brown and flaky.
As soon as the baklava comes out of the oven, pour the cooled syrup all over the top and allow it to soak in as it cools. Cut and serve with vanilla or coconut ice cream.