Pour the chicken broth into a saucepan with the onion and garlic; bring to a boil and cook at a boil until the liquid reduces by half, about 10 minutes. Pour in the white wine, return to a boil, and reduce the liquid by half again, about 10 minutes. Stir in mushrooms, rosemary, and sage; simmer until the mushrooms are tender and have given up their juice, about 15 more minutes. Stir in cream, butter, lemon, and capers; reduce heat and simmer the sauce until thickened, about 10 minutes (45 minutes in all).

Preheat oven to 350 degrees F (175 degrees C).

Place the cornstarch into a shallow bowl and press the chicken thighs into the cornstarch on all sides until thoroughly coated. Shake off excess cornstarch. Heat the olive oil in a skillet over medium heat; pan-fry the chicken thighs until they develop a golden brown crust, about 8 minutes per side. Place the chicken thighs into a 9x9-inch baking dish and pour the sauce over the chicken.

Bake in the preheated oven until the sauce is bubbling and the chicken is no longer pink in the center, about 15 minutes. An instant-read thermometer inserted into the center of a chicken thigh should read at least 165 degrees F (74 degrees C).