Scrub the potatoes in cold water. Halve or quarter any large potatoes so they are all roughly the same size. Snap the woody ends off the asparagus. Trim them so the ends are neat.
Finely grate or pare the zest of the lemon. Juice it. Pick the leaves off the tarragon sprigs. Put to one side.
Pop your chicken breasts on your chopping board. Slice through it horizontally to make two equal-sized steaks. Set them between two sheets of cling film. Bash with a rolling pin to make four thin steaks around ½ cm thick.
Fill a pan with hot water from the kettle. Bring it to the boil. Add the potatoes and simmer for 10 mins or till the potatoes are almost cooked.
While the potatoes are cooking, rub 1 tsp olive oil into each chicken steak. Season. Heat a griddle or frying pan. Add the chicken steaks to the pan. Fry for 4-5 mins till golden brown. Flip. Fry for another 4-5 mins till they are golden and cooked through.
Put the cooked chicken steaks onto a plate. Cover with foil. Leave to rest for a few mins. Add the cherry vine tomatoes to the frying pan. Fry for 4-5 mins till they are a little charred. Turn every now and then.
Add the asparagus to the boiling potatoes. Simmer for 3-4 mins till the potatoes and asparagus are tender. Drain well.
Whisk the lemon juice with 2 tsp olive oil and some salt and pepper. Tip the potatoes and asparagus back into the pan. Add the lemon dressing, lemon zest and tarragon. Toss to mix. Serve with the chicken steaks.