Heat half of the butter in a pan over a medium to high heat. When the butter is foaming, add the pears. Season, to taste, with salt and freshly ground black pepper, then stir well to coat the pears in the butter.
Add the sugar and stir until the sugar has dissolved and caramelised and has coated the pears.
Meanwhile, heat the oil and the remaining butter in a separate frying pan. When the butter is foaming, add the pigeon breasts and fry for 1-2 minutes on each side. Season, to taste, with salt and freshly ground black pepper.
Add the thyme and cooked bacon and continue to cook for a further 2-3 minutes, or until the pigeon breasts are browned on all sides and cooked to your liking and the bacon has warmed through.
To serve, place one slice of grilled baguette into the centre of each of four serving plates. Place a handful of baby watercress leaves on top of each. Spoon over some of the pears, then the pigeon and bacon mixture.