Preheat the oven to 200°C.
Butcher the pigeon into breasts, legs, wings, and giblets, then chop leg meat and giblets for stuffing.
Brown pigeon bones, carrot, onion, and parsley in oil, then simmer with stock, port, and wine until reduced.
Sear pigeon breasts in olive oil skin-side down until golden and set aside.
Mix sausage meat, herbs, pistachios, leg meat, and giblets, then sandwich between breasts.
Fry shallots in butter, cover with chicken stock and thyme, and bake for 30 minutes until tender.
Wrap the pigeon breasts in rolled pastry, seal, brush with egg wash, and bake for 30 minutes.
Combine the reduced sauce with the shallots and heat through.
Remove the Wellington from the oven and rest for several minutes.
Slice the Wellington and serve with the glazed shallots.