Cook four eggs in a saucepan of boiling water for 4 minutes, until soft-boiled. Cool in cold water and carefully peel.
Beat the remaining egg in a shallow bowl. Put the flour in a second shallow bowl and season. Put the breadcrumbs in a third shallow bowl. Roll each boiled egg in the flour, then the beaten egg, then the breadcrumbs.
Fill a deep-fat fryer or a large, deep, heavy-bottomed pan two-thirds full with the vegetable oil. Heat to 180C (a cube of bread should turn brown in one minute when dropped in.) CAUTION: Hot oil can be dangerous. Do not leave unattended. Deep-fry the eggs for 3–4 minutes, until golden
Meanwhile, blend the defrosted peas with the warm ham stock in a food processor. Pass the purée through a fine sieve. It should have the consistency of double cream.
Blanch the fresh peas and mangetout in boiling water for 30 seconds. Drain and refresh under cold water.
In a bowl, mix together the blanched peas and mangetout, ham, pea shoots, mint and Parmesan. Dress with the olive oil and a squeeze of lemon juice. Check the seasoning.
To serve, spoon the pea purée into the bottom of four serving dishes. Pile on the ham salad and top with the crispy eggs.