Fill a large pot with salted water. Add the new potatoes and boil until the potatoes are cooked through, about 15 minutes, although this will vary with the size of your potatoes. The potatoes are cooked when a knife can be easily inserted. Drain and set aside to cool.
Bring a medium pot of salted water to a boil. Add the peas and simmer until cooked, about 5 minutes. Transfer to an ice bath using a slotted spoon.
Halve or quarter the potatoes and place in a large bowl. Drain the peas and add to the potatoes. Add half the goat cheese, the mint, olive oil and a couple twists of salt and pepper. Toss gently and transfer to your serving dish. Top with the rest of the goat cheese. Enjoy immediately or cover with plastic wrap and keep in the fridge until ready to serve.