Put the breast fillets in the wine, add the thyme leaves and shallot. Marinate for about an hour.
Heat some olive oil in a large frying pan. Season the pigeon breasts with salt and pepper, then seal them on each side for a minute or so then transfer them to a plate.
Add the marinade, blackberries, orange juice and a knob of butter to the same pan. Cook for about ten minutes until you get a silky sauce. Add some honey or maple syrup and reduce the sauce until it’s a sticky and thick.
Put back the pigeon breasts - add a drop of wine or orange juice, if the sauce is too thick. Remove the onion and bay leaf, then coat the breasts well with the sauce and cook them for a couple of minutes. (Make sure, you don’t overcook them - otherwise they’ll be rubbery).
Serve the pigeon breasts with the jus.