Heat olive oil in a nonstick saucepan over medium heat. Add fennel, onion, water, and garlic; cook and stir until onion starts to soften, about 5 minutes. Stir in rice until coated with oil and lightly toasted, 1 to 2 minutes.
Stir 1 cup broth into the saucepan; cook until rice absorbs broth, about 5 minutes. Add broth a ladleful at time, stirring until rice is tender and creamy, 15 to 20 minutes in all. Stir in black beans; cook until heated through, about 5 minutes.