Preheat oven to 205°C. Melt the butter in a frying pan over high heat. Seasonpigeon halves with salt and pepper. Brown one side. Turn the halves over and place the pan in the oven. Bake for 7 minutes.
Place the baked pigeon halves on a plate, tent with foil, and set aside to rest for five minutes.
Sweat the shallot in butter in a saucepan over low heat. Add the Madeirawine and reduce almost totally. Add the fond de pigeonneau (squab stock) and reduce substantially. Strain and return the sauce to the saucepan. While the pigeon is resting, continue to reduce the sauce until thickened. Taste the sauce and season with salt, as required.
Also, place the serving plates with the vegetables in the oven for a couple of minutes until the vegetables are reheated.
When the meat has rested, slice each half on the bias in four places. Arrange the pigeon slices on the serving plates. Top with the reduced sauce.