1Remove the rabbit from the refrigerator 10 minutes before cooking. Pat the pieces very dry with paper towels – this helps them brown nicely.
2Peel the carrots and cut them into thin halves (3-4 mm thick). Finely chop the onion. Wash the mushrooms and cut them into quarters. Mince the garlic.
3In a large bowl, mix the mustard, oil, salt, and pepper. Coat the rabbit pieces evenly with this mixture.
4Preheat the air fryer to 190°C (375°F) for 4 minutes.
5Place the rabbit pieces in the air fryer basket in a single layer without overlapping (cook in two batches if needed). Tuck the bay leaf and thyme among the pieces.
6Cook at 190°C (375°F) for 14 minutes. Halfway through, turn the pieces for even browning.
7Reduce the temperature to 175°C (350°F) and cook for another 9 minutes, until the rabbit is golden and tender.
8While the rabbit rests (loosely covered with foil), place the carrots, onion, mushrooms, and garlic in the air fryer basket. Season lightly with salt.
9Cook the vegetables at 185°C (365°F) for 9 minutes, shaking the basket halfway through. Set them aside with the rabbit.
10For the sauce: pour the wine directly into the air fryer pan (turned off). Scrape the pan well with a spoon to deglaze, then transfer the liquid to a saucepan.
11Add the chicken broth and simmer over medium heat for 6-8 minutes, until the sauce coats the back of a spoon.
12Reduce the heat, stir in the heavy cream, and cook for 1 minute. Taste and adjust with salt, pepper, and possibly a bit more mustard.
13Arrange the rabbit and vegetables on a platter, pour the sauce over, and serve immediately.