Ice cream: Dissolve the sugar in the water, then cook for 5 minutes over high heat. Leave to cool. Beat the eggs, add the oil in a trickle then the syrup, salt and milk. Transfer the mixture to an electric ice-cream maker and turn on until set.
Cake: Beat the eggs in an electric mixer until they have tripled in size (up to 15 minutes) together with the sugar and orange zest. Add the oil and yogurt, then carefully fold in the flour mixed with the baking powder and salt. Grease and flour a ring mold or individual molds and fill three-quarters full with the preparation. Bake at 350 degrees F for 30 minutes for small cakes and 45 minutes for one large cake.
Syrup: Dissolve the sugar in the water and cook for 5 minutes over a hot flame. Add the liqueur. Blanch the orange peel in salted water for 5 minutes. Add to the syrup and cook for another 5 minutes.
Crisps: Dissolve the sugar in the water in a thick-bottomed pan and heat. When it begins to turn to caramel, stir so that it colors evenly. Pour onto a greased work surface forming fan shapes.
Pour the syrup over the cake, place the ice cream in the center and decorate with the crisps and cooked orange julienne.
Note: The Hojiblanca oil that is the basis for most oils from Malaga is the perfect ingredient for this cake. Arbequina oil is preferable for the ice cream because it is sweeter and has a nutty flavor that perfumes the creamy egg mixture.