Step 1

For the simple syrup: Put the granulated sugar and 1 cup water in a medium saucepan over medium-high heat and bring to a simmer. Lower the heat to medium and simmer until the syrup has thickened a bit, about 15 minutes. Set the syrup aside to cool completely.

Step 2

For the baklava: Meanwhile, preheat the oven to 350 degrees F.

Step 3

Put the walnuts and granulated sugar in the bowl of a food processor and pulse, stopping every few pulses to scrape down the sides, until finely chopped. Be careful not to overprocess into walnut butter.

Step 4

To assemble the baklava: Unroll the phyllo sheets and cover them with a kitchen towel to prevent them from drying out. Brush the bottom of a 9-by-13-inch pan with the butter and add 1 phyllo sheet. If your phyllo sheets are larger than the pan, simply fold them; there is no need to cut them. Brush with butter and top with another phyllo sheet. Repeat until you've layered half of the phyllo sheets and each sheet is brushed with butter. Sprinkle with the walnut mixture and top with the remaining phyllo sheets, brushing each sheet with butter, including the top sheet. Cut the pastry into 24 squares. Pour the remaining butter evenly over the baklava.

Step 5

Bake until the top is crispy and golden, about 1 hour. Let sit for 10 minutes.

Step 6

Mix the simple syrup with the milk and pour it evenly over the baklava. Let sit at room temperature until cooled completely and the syrup has soaked in, about 2 hours.

Step 7

For the topping: Mix the cocoa powder with the confectioners' sugar and sift it over the baklava. Top with the ground pistachios and chocolate shavings, if using, before serving.