Preheat oven to 350˚F (180˚C).
Lightly brush the bottom and sides of a 9x13 inch (23x33 centimeter) baking dish with the melted butter.
Arrange the phyllo sheets in a single layer on work surface. If needed, trim the edges with a sharp knife to fit the bottom of the baking dish. Cover the phyllo sheets with a large towel when not in use to keep them from drying out.
Carefully place one phyllo sheet on the bottom of the prepared baking dish. Brush the sheet lightly with the melted butter.
Repeat adding phyllo sheets and brushing with butter to create a bottom layer with 8-10 sheets.
Spread about 1/2 of the finely chopped pistachios evenly across the top of the phyllo.
Place another sheet of phyllo over the pistachios and brush with butter.
Repeat again by adding phyllo sheets and brushing with butter to create a second phyllo layer with 8-10 sheets.
Spread the remaining 1/2 of the finely chopped pistachios evenly across the top of the phyllo.
Place another sheet of phyllo over the pistachios and brush with butter.
Repeat again by adding phyllo sheets and brushing with butter to create a final top phyllo layer with 8-10 sheets.
Brush the top sheet of phyllo with butter.
Use a sharp knife to cut through the layers and create individual squares, rectangles, or diamonds.
Place in the preheated oven and bake until the top is golden, 35-45 minutes.
Remove from the oven and immediately cover evenly with the cooled syrup.
Allow the Baklava to cool to room temperature and absorb the syrup before serving, at least 2 hours to overnight.
Serve the squares topped with an additional sprinkling of finely chopped pistachios if desired.
Store in an airtight container at room temperature for up to 4 days.