Bring a large pan of salted water to the boil. Add the mint and the potatoes, then bring back to the boil and simmer for 15 minutes, or until tender. Drain and discard the mint.
Meanwhile, steam or boil the carrots for 2-3 minutes, until just starting to soften, then add the spring onions and peas and cook for 1 minute more.
To make the dressing, put all the ingredients in a small pan and gently heat for 1-2 minutes, stirring occasionally until warmed through.
Put the potatoes, carrots, spring onions and peas in a large serving dish and pour over the warm dressing. Toss to combine and serve.