To make your salsa verde, finely chop the garlic and put in a bowl. Add the capers, gherkins, anchovies, parsley, basil and mint. Mix in the mustard and 1 or 2 tablespoons of red wine vinegar, then 3 good lugs of olive oil, adding more if needed to make a loose mixture.
Put your potatoes into a large pan of salted, boiling water and cook for 12 minutes with the lid on. Put the sole fillets into a clean plastic bag and season nicely with salt and pepper and a small handful of flour.
Toss around until all the fillets are well coated. Just before you start cooking the fish, put your broccoli into a colander, place on top of the potato pan, cover with the lid and steam for 4 minutes or so until cooked.
While the broccoli is steaming, heat a lug of olive oil in a large non-stick frying pan and quickly but carefully put your fillets in so they all cook at the same time.
Cook for a couple of minutes until beautifully golden, then, starting with the fillet that went in first, turn them all over.
Once you've done that, add the butter to colour and flavour the fillets. Cook for no more than another 2 minutes. When the fillets are golden on both sides, remove the pan from the heat.