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Tip the peas into a bowl, cover with cold water and leave to soak overnight.
Heat the oil in a medium saucepan. Add the onion and carrot and fry over a low heat for 10-15 mins, or until soft and translucent but not brown.
Drain the peas and tip into the saucepan with the bay leaf and thyme. Cover with about 1 litre cold water, bring to the boil and skim off any foam. Reduce the heat to a simmer and cook, stirring often, for 2 hrs 30 mins, or until the peas are soft, adding more water as needed (you may need to add about 500ml). Remove and discard the bay leaf and thyme. Blitz with a hand blender until smooth, then stir through the vinegar and butter. Season with sea salt and some black pepper, then serve with thick slices of roast ham.