Using a mortar and pestle, ground the pistachios until coarsely minced. You can also chop them by hand with a sharp knife. You can use a food processor if you prefer but be extra cautious not to ground them too fine. The food processor method is not the most ideal because it releases the nut's oils and changes the baklava flavor.
Heat oven to 400° F.
Brush the inside of a deep 10-by-15-inch baking pan with butter.
Trim the phyllo sheets with scissors to fit the bottom of your baking dish. Always cover phyllo layers with a lightly damp kitchen towel and keep covered.
Place 2 pieces of phyllo on the bottom of the baking pan; drizzle with butter.
Spread the broken pistachios on the phyllo in an even layer, then layer with the remaining phyllo, using the same drizzling method with butter every two sheets until 20 or so sheets are used.
Carefully, using a sharp knife, score the pastry into square or diamond shape pieces. Make sure to cut all the way through to the bottom of the pan. Pour the remaining butter evenly all over the pan.
Bake baklava until the top is golden brown, for about 45 minutes, but it could take an hour or a little more depending on your oven.
When the baklava is baked through and has a lovely golden brown color, remove it from the oven and let it cool a little. Meanwhile, prepare the syrup. Keep oven hot.