Simmer pickling ingredients, add carrots for one minute, then cool and marinate overnight.
Fry shallots, garlic, and bacon in butter for several minutes.
Add split peas and stock, simmering for 40 minutes until tender and thickened.
Preheat the oven to 180°C.
Brown the pork tenderloins in an ovenproof pan with oil.
Add butter and rosemary, then roast in the oven for 8 minutes.
Baste pork with lemon juice and butter before resting for 10 minutes.
Sweat shallots in butter, add peas and milk, and simmer for 6 minutes.
Drain the peas and reserve the cooking milk.
Blend peas, garlic, and mint while gradually adding reserved milk.
Sieve the purée and season with salt and pepper.
Plate the purée, pudding, and pork, garnished with carrots, pea shoots, and oil.