Trim off stems and base. If the feathery fronds are in good shape, roughly chop and reserve to use for garnish. You can either peel the outer layer with a peeler or paring knife; or if too bruised, remove the outer layer completely.
Halve the bulb, cutting from the base through the top, then set the halves face down and cut each half lengthwise into 3 or 4 strips, around 3/4" (2cm) thick.
Braise:
Place a stainless steel skillet, just big enough to accommodate all the slices in one crowded layer, over medium heat. Add just enough olive oil to barely coat the pan. Sprinkle a dash of salt over the oil, add the fennel slices, then sprinkle with more salt. With tongs or your hands, rub the fennel slices in the oil, then flip them over so that both sides are lightly covered in oil.
Lower the heat to low, cover with a lid, and let cook undisturbed for around 5 minutes. You want the fennel to release its own juices to cook in, and cook without browning, until softer yet still firm. Don't overcook, or they will be hard to serve without falling apart.
Caramelize:
Uncover the pan, increase the heat to medium-high and without stirring, let cook around 5 minutes more, until the bottom of the pan surrounding each slice of fennel has turned golden brown. Do not let your eyes off it. If needed, rotate the pan so it sits on different hotspots of the burner to even out the caramelization. Adjust the heat if too high. The bottoms should become deeply golden. Don’t worry that the top of the fennel isn’t getting caramelized. You don’t need to flip it (unless you need to keep a slice from burning).
Cover with a lid, and immediately take off the heat. Let the fennel sweat in this sauna, untouched, for about 5 minutes before opening the lid.
Uncover and immediately stir the fennel wedges with a wooden spoon to coat them in the beautiful caramelized glaze that has released from the bottom of the pan.
To serve, garnish with the chopped fennel fronds.
Reheating: Caramelized fennel reheats well. The best way is in the oven at around 350°F (180°C).
Variations
Fennel seeds - Sprinkle a spoonful in the pan while cooking, or on top as garnish, for an extra touch of fennel flavor.
Goat cheese, sheep's ricotta salata (dry salted ricotta) or feta - Crumble or grate on top to serve.
Grated Parmigiano Reggiano - This is great to sprinkle on top before reheating.