Peel and finely chop the onion. Peel and dice the potato. Put a pan on a medium heat and warm for 1 min. Add 1/2 tbsp olive oil, the onion and potato. Season with a pinch of salt and pepper. Cover, turn the heat right down and gently cook for 10 mins till the veg have started to soften. Stir now and then.
While the onion and potato sweat, peel the carrots. Dice them. After the veg have sweated for 10 mins, stir in the carrots with a pinch more salt and pepper. Add half the tarragon sprigs. Put the lid back on and sweat the veg for another 10 mins till soft. Stir every so often to stop them sticking.
While the veg sweat, crumble the stock cube into a heatproof jug. Add 800ml boiling water. Stir to dissolve the stock cube. Finely chop the remaining tarragon leaves.
Pour in the hot stock. Bring to the boil, then turn the heat down and simmer for 5 mins til the veg are soft. Finely grate in the orange zest. Squeeze in the juice.
Ladle the soup into a blender and blitz till smooth, or use a hand-held blender in the pan.
Taste the soup. Add a pinch more salt and pepper if you think it needs it. Ladle into warm bowls. Scatter over the chopped tarragon and serve.