Preheat oven to 180 C / Gas 4. Grease a traybake tin with tahini.
Combine boiling water and aniseeds in a glass measuring cup; let steep, about 5 minutes. Strain into a bowl; stir in sugar until dissolved. Discard aniseeds.
Mix flour, turmeric, baking powder and ground aniseed powder together in a bowl. Make a well in the centre; mix in oil and butter. Stir in sweetened anise water until batter is the consistency of thick yogurt.
Pour cake batter into the prepared traybake tin. Score top into diamond shapes with the tip of a knife; place 1 pine nut in the centre of each diamond.
Bake in the preheated oven until top is lightly browned, about 30 minutes.