Combine chicken, garlic, 1 tablespoon wine, 1 1/2 teaspoons cornstarch, 1/2 teaspoon salt, and pepper in a medium bowl; toss to coat. Add 1 teaspoon oil, and toss until chicken is lightly coated; set aside. Whisk together broth, cream, remaining 2 tablespoons wine, and remaining 4 teaspoons cornstarch in a small bowl until cornstarch is completely dissolved; set aside.
Heat a 14-inch flat-bottomed wok or a 12-inch skillet over high until a drop of water evaporates within 1 to 2 seconds of contact. Swirl in 1 tablespoon oil. Add chicken; spread in a single layer. Cook, undisturbed, 1 minute, until chicken begins to sear. Continue cooking, making quick scooping motions with a metal spatula, constantly tossing and tumbling (stir-frying) the chicken until it is no longer pink but not cooked through, about 1 minute.
Swirl remaining 1 tablespoon oil into wok. Add asparagus, carrots, thyme sprigs, and remaining 1/2 teaspoon salt; cook, stir-frying constantly, until asparagus turns bright green, 1 minute to 1 minute and 30 seconds. Whisk broth mixture, and pour into wok; cook, stir-frying constantly, until well combined, about 30 seconds. Cover wok with a baking sheet, and cook until sauce comes to a full boil and starts to thicken, about 1 minute. Uncover; add scallions and parsley. Cook, stir-frying constantly, until chicken is cooked through and sauce is thickened, 30 seconds to 1 minute. Discard thyme sprigs. Season with salt to taste.\
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