Trim the fennel and roughly chop 1 tablespoon of the fronds. Halve each bulb through the core, then cut lengthwise into ½-inch-thick slices.

Place a large skillet over medium-high heat and add just enough oil to coat the pan. When hot, cook half the fennel, without moving, until browned, about 3 minutes. Flip and cook 1 minute more. Transfer to a bowl and season with salt and pepper. Repeat with the remaining fennel, adding more oil to the pan if needed.

Return the skillet to medium-high heat. Add the fennel, broth, lemon rind and juice and bring to a boil. Simmer, covered, until tender, about 10 minutes. Using a slotted spoon, transfer to a bowl. Raise the heat to high and reduce the sauce until syrupy, 3 to 5 minutes.

Fold the sauce and reserved fronds into the fennel and top with parmesan or gruyere cheese. Serve warm or at room temperature.