To cook the fennel, gather the olive oil and lemon. Preheat a large fry pan over medium-high heat. Once hot, add the olive oil, followed by the fennel and a good pinch of salt. Toss to combine and let cook for a few minutes. As the fennel cooks and starts to color, toss occasionally until it starts to caramelize. Then add the shallots, stir together and continue to cook until the fennel softens a bit more, about 3 to 5 minutes.
If the pan seems to be getting too brown before the fennel has cooked through, just add a touch of water. Once the fennel has caramelized and softened, but still has a bit of crunch, add the garlic and let cook for another 30 seconds or so. Then turn off the heat and deglaze with the lemon juice. Grate some fresh parmesan cheese over top and toss. Taste for seasoning and top with more a bit more parmesan cheese, if desired. Serve immediately.
Sautéed fennel goes well with many meat, fish and pasta dishes.