Cut the potatoes in half.
Cook the halved potatoes in boiling salted water until just tender to the bite. DO NOT allow them to overcook and turn mushy. They must be able to retain their shape.
When the potatoes are done, drain them well then tip into a large mixing bowl. Add all the other ingredients but only half of the lemon juice. Toss well to coat each piece of potato with the herbs and seasonings. Even if the butter is cold, it will melt in the heat of the newly cooked potatoes.
Leave the potatoes to soak in the oils, herbs and seasonings. After about 15 minutes, taste a piece of potato. Add more lemon juice, salt or pepper, or all of them, if needed.
Serve the potatoes as a finger food, as a snack, as a side dish or as a delicious warm salad.