Prepare the filling.
Place the pistachios, 2 tablespoons sugar, and 1 tablespoon ghee in a food processor. Pulse until finely chopped but not pasty. Set aside.
Prepare the pan and phyllo.
Preheat the oven to 325°F (160°C).
Choose a rimmed baking tray that fits your phyllo sheets, trimming the sheets if needed. A half sheet tray works if your phyllo is large enough to cover it.
Brush the bottom of the tray with a little of the melted ghee. Keep the remaining phyllo covered with plastic wrap and a lightly damp towel while you work.
Build the bottom layers.
Arrange half the phyllo sheets in the tray, brushing each sheet lightly with melted ghee.
Gently prick the bottom stack in a few places with a fork. Drizzle about 1/4 cup of the measured melted ghee evenly over the layers.
Add the pistachio filling.
Spread the pistachio mixture evenly over the phyllo, gently leveling it without packing it tightly.
Finish layering and cut.
Place the remaining phyllo sheets over the filling, brushing each lightly with ghee. Budget the remaining ghee so you have some left for the top.
Using a sharp knife, cut into squares or diamonds, cutting all the way through to the bottom. Pour any remaining ghee evenly over the top and along the cuts.
Bake until crisp.
Bake for 60–90 minutes, until the pastry is deeply golden and crisp. Begin checking at 60 minutes. If the top browns too quickly, loosely cover with foil while the lower layers finish baking.
Make the syrup.
Prepare the syrup early in the baking time so it has time to cool.
Combine the sugar and water in a saucepan. Heat, stirring until the sugar dissolves, then bring to a boil.
Reduce the heat and simmer for 5–7 minutes. Remove from the heat, stir in a squeeze of lemon juice, and let cool to room temperature.
Add the syrup and rest.
As soon as the baklava comes out of the oven, slowly spoon the cooled syrup over the hot pastry, distributing it across the surface and along the cuts. Add gradually, pausing to let it soak in rather than leaving a deep pool.
Let rest uncovered for at least 4 hours, preferably overnight, before serving.