To make the pea sorbet, bring the liquid glucose and 200ml/7fl oz of water to boil in a saucepan to make a stock syrup. Add the frozen petit pois and mint. Allow to cool slightly and then pour into a food processor or blender. Process on high speed to make a purée. Chill, then pour into an ice cream machine and churn for 20-30 minutes or until the sorbet reaches a soft-scoop ice cream texture. Taste for seasoning and adjust with a pinch each of sugar and salt if necessary. Transfer to a freezer container and freeze.
Next, poach the eggs. A rice cooker is the best thing to use, but if you don't have one, heat a pan of water to around 62C/143F, ideally monitoring the temperature with a digital probe. Carefully add the eggs in their shells and leave at 62C/143F for about 1½ hours - the whites will be just firm and the yolks runny. Remove the eggs with a slotted spoon and set aside.
Preheat the oven to 180C/350F/Gas 4. Arrange the bread slices on a large baking sheet, brush with olive oil and bake for about 12 minutes or until golden-brown.
Pour the chicken stock into a medium saucepan and add the butter, shelled peas and a good pinch of salt. Simmer gently for 3-4 minutes to braise the peas until tender.
To serve, carefully peel the shells from the duck eggs. Spoon the braised peas into the centre of warmed shallow soup bowls. Sit the eggs on top of the peas. Lay a slice of ham over each egg, and arrange a spoonful of pea sorbet to one side. Lay a couple of pieces of toast on top of the ham. Dress the pea shoots with a drizzle of olive oil and a sprinkling of salt, then scatter them all around.