Combine the honey, 4 dl water, and star anise stars in a 20 cm saucepan. Bring to a boil over medium heat.
Peel the apples, leaving the stems intact, and rub each one with the lemon half to prevent browning. Gently add them to the boiling syrup and simmer uncovered on low heat for 30 minutes, turning occasionally for even cooking.
Drain the apples and transfer to a deep serving dish. Continue reducing the syrup over medium heat for 5 minutes until it forms small bubbles. Pour the thickened syrup over the apples.
Serve warm or hot for the best flavor—they're also delicious chilled or even iced.
Pair with homemade almond tuiles: In a bowl, whisk together 1 tablespoon flour and 80 g caster sugar. Stir in 25 g melted butter, 120 g slivered almonds, and 2 egg whites until smooth. Refrigerate the batter for 12 hours.
Preheat oven to 175°C (th. 5). Spread the chilled dough into very thin discs or strips on a non-stick baking sheet or parchment paper. Bake for 7-8 minutes until golden.
Working quickly while still soft and pliable, lift with a spatula and drape over a rolling pin for small tiles, a bottle for larger ones, or twist strips around a spatula handle. They’ll harden into beautiful shapes as they cool on a wire rack.
