Prepare the syrup: Add water, sugar, vanilla extract and lemon juice in a saucepan over medium-high heat, bring to a boil.
Then reduce the heat and let it simmer for 15 minutes. Turn off the heat and let it cool completely.
Prepare the nuts: In the food processor, add pistachios, almonds and hazelnuts and blitz a few times until they are finely chopped and have some tiny chunks.
Make baklava: Preheat the oven to 180C / 350F.
Grease the bottom and the sides of a 20x30 cm baking pan with butter.
Put one phyllo sheet in the pan and brush it with the melted butter. Then, put another phyllo sheet over it and brush it with butter, too. Repeat until you have 10 sheets in total.
Sprinkle about ½ cup of chopped nuts on top evenly.
Repeat the previous until you have 4-5 layers of nuts (based on how many phyllo sheets you have).
Brush the top with butter, cut the baklava tray diagonally using a sharp knife.
Bake it for 20-25 minutes or until the top is golden brown.
Remove it from the oven, pour the cooled syrup over it. Allow it to sit for 10-15 minutes. Then serve!
Notes
Cover your phyllo pastry sheets with a kitchen towel; otherwise, they will dry out and become so hard to work with.