Heat 1 tablespoon oil in a large skillet over medium-high heat. Season sliced chicken with ¼ teaspoon each salt and pepper. Add to the pan and cook, turning once, until just cooked through, 5 to 7 minutes. Transfer to a plate and tent with foil to keep warm.
Reduce heat to medium. Add the remaining 1 tablespoon oil, ¼ cup shallot and the minced garlic to the pan. Cook, stirring, until fragrant, about 30 seconds. Add ⅓ cup wine, scraping up any browned bits. Add 1 pound baby spinach in batches; cook, stirring often, until wilted, 3 to 5 minutes.
In a measuring cup, whisk ⅓ cup cream, 2 teaspoons cornstarch and the remaining ¼ teaspoon each salt and pepper. Add to the pan with the spinach; cook, stirring frequently, until thickened, about 2 minutes. Serve with the chicken.
