Prepare the Duck Breasts:

1. Score the Skin: Use a sharp knife to gently score the duck skin in a crosshatch pattern, being careful not to cut into the meat.
2. Season: Generously season both sides of the duck breasts with salt and pepper.

Sear the Duck Breasts:

3. Heat the Pan: Place a large skillet over medium heat. No oil is needed as the duck will render its fat.
4. Cook Skin-Side Down: Place the duck breasts skin-side down in the cold pan. Cook for 6-8 minutes, or until the skin is golden brown and crispy.
5. Flip and Finish Cooking: Flip the duck breasts and cook for an additional 2-4 minutes, depending on your desired doneness. Remove the duck from the pan and let it rest for 5 minutes.

Prepare the Cipollini Onions:

6. Caramelize the Onions: In the same pan, drain excess duck fat, leaving about 1-2 tablespoons. Add the olive oil and butter, then stir in the peeled cipollini onions and sugar. Cook over medium heat until the onions are golden and caramelized, about 8-10 minutes.
7. Deglaze the Pan: Add the balsamic vinegar and scrape up any browned bits from the bottom of the pan. Stir in the honey and fresh thyme.
8. Simmer: Pour in the chicken or duck stock and simmer until the onions are tender and the sauce thickens slightly, about 5-7 minutes.

Assemble the Dish:

9. Slice the Duck: Slice the duck breasts thinly, against the grain, to ensure tenderness.
10. Serve: Arrange the duck slices on a platter or individual plates. Spoon the caramelized cipollini onions and sauce over the top.