Pour the honey into a saucepan 20 cm in diameter. Add 4 dl of water and the anise stars. Bring to a boil.
Peel the apples, leaving the stems. Rub each apple with the lemon half. Plunge them into the boiling syrup and cook for 30 minutes at a low simmer, uncovered, turning the apples from time to time.
Drain the apples and put them in a deep dish. Reduce the cooking syrup for 5 minutes over medium heat, until small bubbles form. Drizzle over apples.
Serve these apples hot or warm. They are also very good cold and even iced.
Serve the apples with almond tuiles:
Mix 1 tablespoon of flour and 80 g of caster sugar.
Add 25 g of melted butter, 120 g of slivered almonds, 2 egg whites and mix well. l
Leave the dough to rest for 12 hours in the refrigerator, then roll it out into very thin discs or long strips on a non-stick baking sheet or baking paper.
Cook for 7 to 8 minutes in the oven th. 5 (175°C), then lift the tiles with a slotted spatula:they must be soft and elastic.
Lay them astride a rolling pin if they are small or on a bottle if they are large , or even twist the strips on a spatula handle.
Very quickly the tiles will dry, taking on a nice shape.
Let them cool on a wire rack.
