In a large skillet, heat the oil over medium-high heat. Add the shallot and garlic. Cook, stirring, until they become fragrant, about 30 seconds. Stir in the pesto sauce, broth, and cream. Bring the mixture to a simmer and add the gnocchi and cooked shredded chicken. Continue to cook, stirring often, until the liquid has mostly been absorbed and thickened, about two to three minutes.
Stir in the baby spinach and continue to cook until the spinach is wilted, about one minute.
Serve immediately or store in the refrigerator for up to three days.