Cut the chard stalks off just below each leaf and thinly slice the stalks. Chop the chard leaves into large pieces. Keep the stalks and leaves separate.
Bring a large, wide pot of salted water to a boil over high heat. Add the sliced fennel and chard stalks and cook for 3 minutes. Add the chard leaves and cook until tender, 3 to 5 minutes. Drain well in a colander. (The chard can be cooked to this point up to 3 hours ahead.) Rinse and dry the pot.
Finely grate the zest from the lemons and set aside. Cut the top and bottom ends off the lemons, then stand each on a cut end and slice off the peel to expose the flesh. (Try to remove all of the bitter white pith.) Cut the lemon segments from the membranes, letting them drop into a small bowl.
Heat the oil and garlic in the pot over medium heat. When the garlic begins to sizzle, add the fennel fronds (if using) and the lemon segments and cook, stirring often, for 1 minute. Add the chard leaves and stems and fennel and cook, stirring, until heated through. Stir in the lemon zest and season to taste with salt and pepper. Serve, sprinkled with the Parmigiano.