Trim off the fennel stalks. Trim about 2 tablespoons of the frilly, dill-like leaves from the stalks and set aside. Discard the stalks (or save to add to soups or broths). Cut the bulbs into lengthwise quarters, or, if the bulbs are very large, into sixths. Each wedge should be 2 to 3 inches wide and should be held intact with a portion of the core. Set a large (10-inch) skillet over medium heat. If using the saffron, put it in the dry pan and let heat for a couple of minutes. Pour in the olive oil and swirl to coat the bottom of the pan. Add the fennel wedges, flat side down, and season lightly with salt and pepper. Increase the heat to medium high. When the first side is brown, after 3 minutes, turn the fennel and season again with salt and pepper. Brown the second flat side, turn, season, and brown the rounded side the same way. The total browning time should be about 10 minutes.
Lower the heat to medium, give the pan a minute to cool slightly, and then add the pastis, wine, or vermouth. Let the alcohol cook until nearly evaporated, 30 to 60 seconds, and then add the broth or water. Lower the heat to medium low, cover, and simmer gently until the core is tender when pierced with a table fork, 30 to 40 minutes. Turn the pieces every 10 minutes so they cook evenly and, if necessary, add more water, 1/4 cup at a time, to keep the pan from getting dry. (A glass lid makes it easy to monitor the moisture level.) While the fennel cooks, mince the reserved leaves.
Transfer the fennel wedges to a platter, turning them to sit on their rounded sides. If the braising liquid looks watery, boil briefly until it reduces to a syrupy consistency. Drizzle the syrupy juices over the fennel, season to taste with salt and pepper, and sprinkle the minced leaves on top. Serve hot, warm, or at room temperature.