Heat the oven to 200C/fan 180C/gas 6. Boil the potatoes until just tender then drain and slice thickly.
Heat 1 tbsp olive oil in a non-stick frying pan. Add the chicken breasts skin-side down and cook for 4-5 minutes until the skin is crisp and golden.
Flip over and cook on the other side for another 5 minutes and then put on a baking tray in the oven for 5 minutes until cooked through.
Add the shallots to the chicken pan and cook until softened. Tip in the wine and cook until almost evaporated, then stir in the cream, mustard and chicken stock.
When the sauce bubbles, stir in the potatoes and peas and season. Simmer for 3-4 minutes until piping hot, then stir in the tarragon. Spoon into shallow bowls and top with the chicken, cut into slices.