Note: The carrots and fennel can be trimmed and cut up to 6 hours ahead and refrigerated until ready to use, but the dish is best made just before it’s served. It does not re-heat well.
Heat a large, heavy-bottomed skillet over high heat. Add the butter, olive oil, and honey. Stir well and add the carrots, fennel, orange zest, and fennel seeds. Toss until the slices are well coated with the oil. Sauté until the fennel starts to soften, tossing occasionally, about 2-3 minutes.
Add the water, orange juice, and salt. Season with pepper, to taste. Toss quickly and reduce the heat to medium to medium-low. Cover the pan with a lid and simmer until the vegetables are tender, about 10 minutes.
Remove the lid. Increase the heat to high and simmer vigorously until the juices have evaporated and some of the vegetables are golden-brown, about 6-7 minutes, tossing only occasionally so as not to break or mush the vegetables. Remove the orange zest, transfer to a serving platter, top with the fennel greens, and serve immediately.