1. Preheat the oven to 150°C, gas mark 2. Line a large baking tray with baking parchment. To make the cookies, reserve 6 walnut halves and place the remainder in a food processor, blitz until ground. Whisk the yolks and sugar together until pale and thick. Add the vanilla, and then gradually stir in the ground walnuts.
2. Place 12 spoonfuls of the mixture onto the prepared baking tray. Break the reserved walnut halves in two and place on top of each cookie. Bake for 20-25 minutes until just golden at the edges and soft in the centre. Cool on the tray slightly before removing to a cooling rack.
3. Meanwhile, peel the pears, leaving the stalks intact, and cut the bases level so they can stand up when serving. Place the pomegranate juice, sugar, 1 tsp rose petals and cardamom pods in a large saucepan, and bring to the boil. Simmer for 1-2 minutes until the sugar has dissolved. Add the pears and 200ml water. Cover and simmer for 10 minutes until tender.
4. Remove the pears and boil the sauce for 15 minutes or until reduced by half and syrupy. Strain through a sieve. Place the pears onto 4 plates, drizzle with the sauce and garnish with the extra rose petals, pistachios and pomegranate seeds. Serve with the walnut cookies.