Season the chicken tights all over with salt and pepper. In a large skillet over medium-high heat add 1 olive oil and 2 tablespoons butter.
Sauté the chicken tights skin down for 5 - 6 minutes per side if the skin feels some resistance when shaking the skillet, cook it a bit longer. Turn them over and sauté the other side until nicely browned, and no juices are running, 5 to 6 minutes.
Lower the heat under the skillet. Add the brandy and chicken broth to the pan and put it back on the heat and bring it to a boil. Add minced garlic. Cook until garlic is slightly brown and liquid half evaporated about 2 minutes.
Add lemon juice, parsley, and capers and continue cooking for another 3 to 5 minutes.
Finish the sauce with butter and lemons slices. Once the butter melts and thickens the sauce, it is ready to serve.
Garnish with chopped fresh parsley and serve.