Heat 1 tablespoon oil in a large saucepan over medium heat. Add onion and cook, stirring occasionally, until soft, about 5 minutes. Add garlic and cook, stirring, for 30 seconds. Add flour and paprika; stir to coat. Add broth and the chopped broccoli. Bring to a boil over high heat. Reduce to a gentle simmer and cook, stirring occasionally, until the broccoli is tender, 8 to 10 minutes.