Trim the stalks from the fennel. Discard or reserve for a vegetable stock. Quarter each bulb and carve out the core at the base, leaving just a thin portion of the core so the quarters won't fall apart as they cook.

Heat the olive oil in a large skillet over medium-high heat. Working in two batches, add the fennel in a single layer without crowding. Cook for 5 to 7 minutes on each side until golden, shaking the pan from time to time. Set the first batch aside on a plate, add a little more olive oil to the pan, and brown the other batch. Return all fennel pieces to the pan.

Sprinkle with salt and rosemary. Add the wine, stock, and lime juice. Bring to a simmer and cover. Turn the heat to medium-low and cook for 20 to 25 minutes, until tender. Remove the lid, turn the heat up to medium-high, and cook for 5 minutes, until the juices are syrupy. Serve warm, at room temperature, or cold.