For the Lavender Ice Cream:
In a pot, bring the milk and sugar to a boil, stirring until the sugar is dissolved. Remove from the heat and add the lavender flowers. Cover and let cool. Leave to infuse for 8 hours, or overnight in the fridge. Strain the milk. Whip the cream until firm peaks form, then fold it gently into the infused milk preparation. Transfer to the bowl of an ice cream maker, and churn according to the instructions for the machine. Transfer to a container and place in the freezer until ready to use.
For the Fruit Papillotes:
Preheat the oven to 350 degrees F (180 degrees C). Cut four 14-inch (35.5 cm) pieces of parchment paper. Lay them flat on the working surface. In a bowl, combine the fruit with the lime juice, sugar, and vanilla seeds. Divide the fruit between the four pieces of parchment. Add 1/2 vanilla bean and 1/2 tablespoon butter to each papillote. Lift the wider edges of the paper and fold them over the top. Crimp the edges by pleating them over and over, or secure with string. There should be enough space between the ingredients and edge of the paper for the pouches to puff.
Set the pouches on a rimmed baking sheet and bake for about 20 minutes, or until the fruit is soft and has released its juice. To serve, open each papillote, remove the vanilla bean, and put one scoop of lavender ice cream in the middle of the fruit. Or serve with whole milk Greek yogurt.