Depending on what you eat before you serve this, you may feel this needs a little straightening out with flaky salt, pomegranate molasses, extra oil or even a few chilli flakes over the top. A shot of gin can soften the texture and the sweetness if you fancy. Thai basil, Korean mint and sweet cicely make fine alternatives to tarragon.
Pour the cream and milk into a medium pan with the half bunch of tarragon that isn’t stripped and bring gently to a simmer.
Meanwhile, put the egg yolks, sugar and tarragon leaves into a blender and blitz on low speed, increasing to high briefly. Add the oil and salt and blend again, increasing the power until a smooth consistency forms.
Pour the hot creamy milk through a sieve into a jug. Turn the blender on low, and pour the creamy milk very slowly into the oily tarragon mixture. When fully incorporated, pour the mixture back into the pan and heat gently, whisking frequently, until it thickens a little. Cover and allow to cool.
Churn in an ice cream maker if you have one, or pour into a plastic tub and freeze for a few hours before spooning into a blender and whizzing briefly, pouring back into the tub and returning to the freezer. Remove from the freezer 20 minutes prior to serving to make it easier to scoop.