Preheat the oven to 180°C.
Fry the chicken breast in olive oil and butter for 2 to 3 minutes per side until brown.
Season with salt and pepper then add lemon juice, lemon wedges, and garlic to the pan.
Roast in the oven for 10 to 12 minutes until the chicken is cooked through.
Remove the chicken, lemon, and garlic from the pan and keep warm on a plate.
Boil the potato for 7 minutes, adding the peas for the final 3 minutes.
Drain the vegetables and mash them with butter.
Deglaze the frying pan with white wine and reduce by half over heat.
Stir in the cream, tarragon, and lemon juice into the pan and season.
Serve the chicken over the mash and drizzle with the tarragon sauce.