How to Make It
Heat oil in a large saucepan over medium. Add onion, garlic, salt, and pepper; cook, stirring often, until onion starts to turn golden brown and garlic starts to soften, about 10 minutes. Add broth; bring to a simmer over high. Reduce heat to medium; cook, uncovered, stirring occasionally, until onion and garlic are very tender, about 20 minutes.
Tear buns into bite-size pieces; add to garlic mixture, stirring to incorporate. Remove from heat; and blend, in batches if needed, until a smooth puree forms, about 2 minutes. Ladle into bowls; top with chives.