- 1Heat the oven to 400°F and arrange a rack in the middle.
- 2Melt 1 tablespoon of the butter in a medium frying pan over medium heat. When it foams, add the shallots, season with salt and pepper, and cook, stirring occasionally, until softened and golden brown. Transfer to a plate and set aside.
- 3Add the port to the frying pan and bring to a boil over high heat. Reduce the heat to medium and continue to simmer until the port is reduced by half, about 6 to 10 minutes. Add the broth and reduce by half again (you should have about 2 cups); remove from heat and set aside. Meanwhile, mix together the reserved shallots, cheese, and 1 tablespoon of the thyme in a small bowl until evenly incorporated. Divide into 6 portions and set aside.
- 4Make pockets in the chicken by laying 1 breast on a cutting board and using a sharp knife to slice horizontally about three-quarters of the way through the meat. Move the knife in a fanning motion to slightly enlarge the pocket (be careful not to cut all the way through); repeat with the remaining chicken breasts. Season the chicken all over with salt and pepper and stuff the divided shallot filling into the pockets.
- 5Heat the olive oil and 2 tablespoons of the butter in a large frying pan over medium-high heat. When the butter foams, add 3 of the chicken breasts and cook until golden brown, about 3 minutes. Flip and repeat. Remove and repeat with the remaining chicken. Once all the chicken is browned, place it on a baking sheet and bake until it’s cooked all the way through (the juices will run clear when pierced with a knife), about 20 minutes.
- 6About 5 minutes before the chicken is ready, melt 1 tablespoon of the butter in a medium frying pan over medium heat. Once it foams, add the figs, cut side down, and the remaining thyme and cook until the figs are well browned. Add the reserved port sauce and the remaining 2 tablespoons butter and stir until the butter has melted and the sauce is heated through. Season with salt and pepper if necessary. When the chicken is ready, transfer to a serving platter, top with the sauce and figs, and serve.
Beverage pairing: Qupé Marsanne, California. Marsanne makes wines with good weight, but also good acidity and subtle, unprepossessing flavors of white peaches and jasmine. It’s lovely with something equally humble like chicken, especially when accented with thyme, the sharpness of chèvre, and the richness of figs.