Heat half the butter in a large frying pan, then fry the bacon for 5 mins until starting to crisp. Transfer to a plate using a slotted spoon. Fry the bread in any leftover bacon fat for 1 min on each side until crisp and golden, then transfer to a plate and set aside.
Season the pigeon generously with salt and pepper, and heat the remaining butter in the pan until sizzling. Sear the pigeon for 2-3 mins on each side until golden, then transfer to a chopping board and leave to rest.
Return the fried bacon to the pan and turn up the heat. Scatter over the mushrooms and fry for 3-4 mins until softened, then add the spinach, season and splash in the vinegar. Turn the heat up to high and stir-fry until the spinach is wilted. Divide the spinach mixture between the fried bread slices. Finely slice the pigeon breasts, arrange over the spinach and serve.