First make the mascarpone ice cream. Pour the cream and milk into a saucepan and bring to a simmer on the stovetop. In a heatproof bowl, whisk together the egg yolks and sugar until pale and fluffy. Pour over a third of the cream and milk, whisking to incorporate, then slowly whisk in the remainder. Pour the mixture back into the saucepan and cook over low heat, stirring constantly until smooth and thickened – when it’s ready, the custard should coat the back of a spoon. Pour into a bowl and leave to cool for 5 minutes before whisking in the mascarpone.
Transfer to an ice-cream machine and churn according to the manufacturer’s instructions. (If you don’t have an ice-cream machine, freeze the ice cream in a shallow container, whisking it every hour to break up the ice crystals, until you are happy with the consistency.)
Cut the peaches in half, remove the stone and then cut each half again so you get four round slices from each peach. Lay the slices on a paper-towel-lined tray or plate in the fridge for 30 minutes to dry a little.
Light the barbecue and set for direct cooking. Throw the wood chips onto the coals, then lay the peach slices on the grill and close the lid of the barbecue.
Cook the peach slices for 5 minutes before turning them over and cooking for a further 3 minutes – they should be soft and well charred.
Meanwhile, take the ice cream from the freezer to let it soften slightly.
Transfer the peaches to a serving platter, drizzle over the honey and sprinkle with the lavender flowers, if you’re using them, then serve with the ice cream.