Preheat the oven to 475 degrees F.

Heat 1 tablespoon of the oil in a saucepan over medium-high heat. Add the shallots to the pan and cook, stirring, for 1 minute. Add the garlic and cook for 30 seconds. Add the figs, wine, and thyme, and cook, stirring, to deglaze the pan. Cook at a brisk simmer until wine has reduced enough to coat the back of a spoon and the figs are tender, 25 minutes. Add the chicken stock and cook again until the sauce is thick enough to coat the back of a spoon, 20 to 30 minutes. Remove the sauce from the heat, add the butter and stir until the butter is melted and the sauce is thickened. Adjust the seasoning, to taste and set aside, covered, to keep warm. Do not allow the sauce to boil or it will separate.

Cut the backbone out of the squab and gently flatten with the palm of your hand. Lightly season the squab on both sides with salt and ground black pepper.

Heat the remaining oil in a large saute pan or skillet over medium-high heat. Add the squab, skin-side down, and cook for 3 minutes. Turn and place in the oven. Roast until the birds are cooked through and tender, about 7 minutes. Remove from the oven, transfer to a platter, and set aside to rest for 5 minutes before serving. Drain the remaining fat from the skillet and add the sauce to the skillet to rewarm, scraping to dislodge any browned particles clinging to the bottom of the pan.

Serve the squab with the sauce ladled over all.

Wine Recommendation: Napa Valley Syrah