Blanch the pigeons in boiling water for two minutes, then remove and discard the water.
Boil the braising sauce ingredients, add pigeons and ginger, and simmer for 30 minutes until tender.
Remove pigeons and let them dry in a cool, airy place for at least two hours until the skin feels like parchment.
Heat oil in a deep-fat fryer or wok and deep-fry the pigeons for 10 minutes until crisp and brown.
Drain pigeons on kitchen paper and let them cool for a few minutes.
Stir-fry peppercorns and salt for one minute, then cool and blend to create a dip.
Stir-fry garlic and salt for 15 seconds, add Chinese greens, and cook for 3-4 minutes.
Add 30ml chicken stock and continue stir-frying until greens are done but still crisp.
Chop pigeons into pieces and serve immediately with lemon wedges, salt and pepper dip, and greens.