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Cook the peas in boiling water for 2-3 minutes until just tender, then drain and refresh in cold water. Pat dry.
Tip the peas into a food processor and add the garlic, pine nuts, parmesan, mint and olive oil. Season with salt and pepper, then pulse very briefly until the ingredients are roughly chopped. Don’t overdo it – they should still have lots of texture. (You can freeze the pesto at this point.)
Cook the spaghetti according to packet instructions until al dente – that’s with a bit of bite still. Drain, reserving some of the cooking water.
To serve, toss the spaghetti with the pesto and about 2 tbsp of the water. Pile into warmed bowls and serve at once, with parmesan and olive oil at the table.