Heat the oil and butter in a large saucepan over a medium-low heat and sweat the onion with the thyme until soft and translucent, about 10 minutes.
Add the stock, peas (reserving a handful to finish the soup if you like) and parsley. Season with salt and pepper, bring to a simmer and cook for 5–10 minutes, or until the peas are very tender.
Cool slightly, then purée the soup in a food processor or blender, or with a stick blender, until very smooth – you may need to do this in two batches if you are using a processor or free-standing blender.
Return the soup to the pan, adjust the seasoning and heat through. Ladle the soup into warmed bowls. If you have some fresh, raw peas, scatter a few on top (or you could use blanched frozen peas). Add the mint, if using, trickle over a little olive or rapeseed oil and serve.
Alternatively, you can let the soup go cold, then chill it lightly before serving – add the scattering of peas and mint, if using, and trickle of oil at the last minute.
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