"Slowly sauteing fennel in wine concentrates its flavor, while a splash of balsamic vinegar at the end adds brightness. This makes a fabulous pizza topping, quiche layer, burger topping, or sandwich condiment. Use your imagination; perhaps a spread made from caramelized fennel and cream cheese?"
Cut white bulb off bottom of each fennel bulb, reserving green tops for other purposes, if desired. Quarter each fennel bulb and remove core. Thinly slice each bulb across the grain.
Melt coconut oil in a cast iron skillet over high heat; saute fennel until lightly browned, 3 to 5 minutes. Season fennel with salt.
Pour 1 to 2 tablespoons wine into the skillet and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Reduce heat to low and simmer, adding remaining wine and water as needed, until fennel is golden brown and tender, about 40 minutes.
Remove skillet from heat and toss fennel with balsamic vinegar.