Scrub the oranges thoroughly.
Wash and pat dry tarragon.
In a freezer-safe tray, add the sugar and zest the oranges over it.
Cut the blood oranges in half.
Over a bowl, remove the orange flesh and keep the intact peel. We will use the peel to serve the granita in.
Extract the juice of the blood oranges by passing the fruit flesh through a sieve. You should have about 400 ml of juice.
Transfer the juice into the tray with the sugar and zest, and mix vigorously, until the sugar dissolves.
Remove the tarragon leaves from the stem and add them to the juice and sugar mix.
Transfer to the freezer for 90 minutes. Once the top layer is frozen, use a fork to scrape the surface. This is to create little crystals. Transfer back into the freezer for a further 90 minutes. Repeat this process one more time: scrape the top and return it to the freezer. After you have completed this scraping-and-freezing process 3 times, or once you have reached the desired texture. Return to the freezer for 1 hour.
After 1 hour, the granita should be ready for serving. Transfer into the empty orange skins and serve immediately.