Trim a sliver off the ends of the fennel bulbs, but not enough so that it falls apart. Then cut the bulb into 1-inch wedges lengthwise (like the wedges of an orange).
In a large, high-sided saute pan, heat 1 tablespoon olive oil over medium heat. Saute onion and garlic for 5-6 minutes, until soft and slightly browned. Stir in coriander and bay leaves, and cook for a few seconds, until fragrant.
Pour in the wine and scrape up any bits stuck to the bottom of the pan. Pour in broth and water, and bring to a boil. Nestle the fennel wedges in the pan, sprinkle with salt and pepper, and cover. Reduce heat to medium-low, so the liquid maintains at a medium simmer, and cook for 30-40 minutes, until the tip of a sharp knife can pierce the stem-end of the fennel easily.
Use tongs to remove the fennel wedges to a plate, and pour off liquid. (The liquid makes a tasty soup base or enhanced vegetable broth.) Return the pan to medium-high heat. Swirl in remaining 2 tablespoons olive oil, and return fennel to pan. Season with salt and pepper. Cook for 5-8 minutes, turning occasionally, until fennel is slightly caramelized on all sides.
Serve warm or at room temperature.