Answer:
The gerund is stargazing.
Step-by-step explanation:
You see, a gerund is a noun that looks like a ing verb. In the sentence, "stargazing" is the only word that ends in ing. The function of the gerund is that it serves as a noun in this sentence. Don't get it confused with the the word "is" as a helping verb of stargazing. In addition to the function, it describes what this person's favorite activity is to do for enjoyment or just relaxing. I hope this helps, and I wish you have a marvelous day!