Prepare the duck:

1. Score the skin of the duck breast in a crisscross pattern (without cutting into the meat).
2. Season with salt and black pepper.
3. Place the duck skin-side down in a cold pan and cook over medium heat for 6-8 minutes, until the skin is golden and crispy.
4. Flip and cook for another 3-4 minutes for medium-rare.
5. Set aside and let the duck rest for 5 minutes before slicing.

Make the orange sauce:

1. In the same pan, remove excess fat, leaving about 1 tablespoon.
2. Add orange juice, zest, honey, balsamic vinegar, and chicken broth.
3. Simmer for 5 minutes, stirring occasionally.
4. Stir in butter to thicken and create a glossy finish.

Roast the vegetables:

1. Preheat oven to 400°F (200°C).
2. Toss Brussels sprouts, potatoes, and cherry tomatoes with olive oil, salt, and pepper.
3. Spread evenly on a baking sheet and roast for 20-25 minutes, until golden and tender.

Serve:

1. Slice the duck breast and arrange on plates.
2. Drizzle with the orange sauce.
3. Serve with the roasted vegetables.
4. Garnish with chopped pistachios and fresh mint.