Bring a large pot of lightly salted water to a boil. Add broccoli and cook uncovered until bright green, about 2 minutes. Transfer broccoli to a bowl of ice water using a slotted spoon and immerse for several minutes to stop the cooking process. Drain.
Bring water back to a boil in the same large pot; add sliced carrot and cook for 1 minute. Drain.
Mix water and cornstarch together in a bowl until smooth. Add chicken granules and salt and mix well.
Heat peanut oil in a wok or large skillet over high heat; saute broccoli and carrots for 2 minutes. Add cornstarch mixture; cook and stir until vegetables are coated evenly, 1 to 2 minutes.