Prep the fennel: Cut off the green tops and trim the base of the fennel bulbs. Remove any tough outer layers. Cut each bulb in half lengthwise through the core, then slice into ½-inch-thick wedges.
Sear the fennel: Heat the olive oil and butter in a large skillet over medium heat. Add the fennel slices and cook for 3 to 4 minutes per side until lightly golden.
Braise the mixture: Pour in the chicken broth and dry white wine. Season with salt and pepper. Bring to a simmer, then lower the heat, cover the pan, and cook for 20 to 25 minutes until the fennel is fork-tender.
Add the cheese: Remove the lid to let any excess liquid evaporate. Sprinkle the grated Parmesan cheese evenly over the top of the warm fennel. Cover the pan for 2 minutes until the cheese melts.
Serve: Garnish with reserved chopped fennel fronds and serve warm.
