Prepare the syrup: Combine 1 1/4 cups sugar, 1 1/2 cups water, and 2 slices of lemon in a saucepan. Stir until sugar dissolves, then stop stirring. Once it comes to a boil, turn off the heat, add 1 tablespoon ghee (optional), and 1 teaspoon vanilla. Set aside to cool.
Roast coconut and powdered milk: In a pan over low heat, mix 1/3 cup coconut with 1 tablespoon powdered milk. Roast until golden, then set aside to cool.
Prepare the basbousa mixture: In a large bowl, mix 3 cups fine semolina with the roasted coconut and powdered milk. Add 150 grams melted ghee and mix lightly. Then, add the milk, sugar, vanilla, and heavy syrup mixture, stirring gently.
Bake the basbousa: Pour the mixture into a greased 30 cm tray, ensuring an even distribution. Optionally, add nuts on top. Refrigerate for 15 minutes, then bake in a preheated oven at 200°C on the middle rack for about 30 minutes until golden, then broil until the top is evenly browned.
Finalize and serve: Immediately after baking, pour the cooled syrup over the hot basbousa. Optionally, spread a spoonful of melted ghee on top. Allow to rest for optimal texture before serving.