Preheat the oven to 350 degrees F.
Beat the eggs in a large mixing bowl on high speed until foamy. Beat in flour, granulated sugar and brown sugar until smooth. Add the 3 sticks of softened butter and vanilla extract, beat until smooth and creamy. Stir in chocolate chips, pistachios and walnuts.
Brush a 9-by-13-inch baking dish with some of the melted butter. Layer 10 pieces of phyllo in the dish, brushing each piece with butter before adding the next (keep the remaining dough covered with a damp towel). Gently spread 1/2 of the cookie dough over the phyllo dough (the layer will be somewhat thin). Layer 10 pieces of phyllo on top, brushing each with butter before adding the next. Spread with the remaining half of the cookie dough. Now add the third and final layer of phyllo dough. Layer on 12 pieces of phyllo right on top, brushing each with butter before adding the next.
Cut into the baklava to make strips, about 1 1/2 inches wide. Then make diagonal slices, about 1 1/2 inches apart, to create a diamond pattern. Bake until golden, about 45 minutes to 1 hour.
Meanwhile, make the syrup. Add the water, brown sugar, vanilla, vanilla bean seeds and the vanilla bean pods to a medium sauce pot. Bring the mixture to a boil, reduce the heat to medium and cook for 10 to 15 minutes. Remove from the heat and remove the vanilla bean pods.
Pour the syrup over the warm baklava and let soak, for at least 6 hours or overnight (I covered my pan after about 2 hours of cooling with plastic wrap). When ready to serve drizzle each piece with melted chocolate and sprinkle with sea salt.