Coat a large saute pan with olive oil over high heat. Sprinkle the squab breasts and legs with salt and pepper. When the pan is hot, place the squab skin-side down into the pan and sear until golden and crispy, about 6 minutes. Flip and continue to cook until the squab is medium rare, 1 minute longer. Transfer to a plate to rest.
Degrease the pan, leaving a couple tablespoons of fat. Add the shallots to the drippings in the pan and sprinkle with salt, scraping up the drippings with a wooden spoon. Saute the shallots until they begin to soften, 1 minute, and then add the mushrooms and saute until they just start to soften up.
Carefully pour in the cognac off the heat, and then return the pan to the heat until the alcohol has completely cooked off and the pan is almost dry. Pour in the marsala and ignite again, allowing the wine to cook until the flame dies down. Add the chicken stock and simmer to reduce the sauce slightly, about 3 minutes.
Return the squab to the pan and simmer gently to heat through, 1 minute. Plate 1 leg and breast per plate. Remove the sauce from the heat and stir in the creme fraiche and butter, whisking until just incorporated. Stir in the parsley and sage. Taste and adjust the seasoning, and then pour the sauce around the squab.