Remove all the "stalks" of the fennel, leaving just the bulb. Remove any hard, weathered outer layers then wash the bulbs and cut into four, from top to bottom (not across).
Heat 2-3 tablespoons of olive oil in a large frying pan over a high heat. Lightly salt the fennel then quickly brown it on all sides. Turn down the heat and add the white wine. Cover and simmer very gently for at least 30 minutes (I prefer about 45 minutes myself) until the wine has been totally absorbed and the vegetable is tender (add a little more wine during cooking if necessary).
Remove the fennel from the pan then deglaze the pan using the balsamic vinegar. Pour the glaze over the fennel and serve immediately.