Heat oil in a soup pot over medium-high heat. Add onion and celery seed. Cook until onion is soft and translucent, about 4 minutes. Pour in broth and bring to a boil. Add gnocchi and cook for 3 minutes. Stir in half-and-half and ½ of the bacon. Remove from heat and stir in ¾ of the Cheddar cheese until melted. Let sit to thicken, about 5 minutes.
Ladle soup into bowls and top with remaining bacon, Cheddar cheese, and chives. Season with salt and pepper.
