In a saucepan over medium-high heat, combine 3 cups of the sugar and the water and heat, stirring to dissolve the sugar, until the mixture is clear and thick. Let the syrup cool.

In a food processor, chop the walnuts, then add the vanilla and the remaining 1 cup sugar. Process again but do not allow the mixture to become mushy. Set the filling aside.

Starting with 1 pound of filo dough, place 1 filo sheet on a baking sheet and drizzle with melted butter. Top with another filo sheet and drizzle with butter. Repeat with the remaining 1 pound of dough. Spread the filling so it covers all of the filo.

Using the second pound of filo dough, repeat the steps above, layering the filo sheets and drizzling with butter. Drizzle the remaining butter over the top of the layers.

Tuck the layers in and around the sides of the pan (this helps hold the filling in place). Place in the freezer for 30 minutes to set the butter. 

Meanwhile, preheat the oven to 315°F. 

Remove from the freezer and cut star shapes in the filo by cutting lengthwise and then across. Bake until golden, about 1 hour.

Remove the baklava from the oven and pour the syrup into all of the cut lines and over the top. Let cool before serving.