Warm a large pan over a medium heat for 1 min. Add 1 tbsp olive oil and the chicken. Cook for 6-8 mins, turning once, to brown all over.
While the chicken cooks, peel and quarter the shallots. Trim the ends from the courgette, halve it lengthways and then thickly slice it. Peel and crush or grate the garlic clove. Peel and dice the potatoes.
Lift the chicken out of the pan and pop onto a plate. Add another ½ tbsp olive oil. Add the shallots and courgette. Season with salt and pepper. Fry for 3-4 mins, stirring often, till softened and beginning to brown. Add the garlic and potatoes and cook for another 1 min.
Crumble the stock cube into a heatproof jug. Add 300ml boiling water and stir. Return the chicken to the pan with any resting juices from the plate. Pour over the stock. Bring to the boil, then cover and simmer for 7-8 mins.
Trim any woody ends off the asparagus and chop the spears into bite-size chunks (see our tip below). Add to the pan, sitting the asparagus on top of the stew – you don’t need to stir it in. Cover and let the asparagus steam for 2 mins till just tender.
Drain and rinse the butter beans. Roughly chop the tarragon leaves, discarding the tough stalks. Stir the beans into the stew with half the tarragon, mixing in the asparagus. Cover and simmer for 2 mins to warm everything through.
Taste the stew and add more salt and pepper if it needs it. Ladle the stew into warm bowls. Garnish with the remaining tarragon to serve.