Preheat oven to 350 degrees F.

Rinse duck breasts, pat dry with clean paper towel, and sprinkle with kosher salt and ground black pepper.

Combine curry paste, coconut milk, beef stock, bay leaves, curry powder, cinnamon stick, allspice, turmeric, coriander, nutmeg, pork broth (1 cup), and water in a medium saucepan and bring to a medium-high heat. Let simmer and reduce while duck cooks.

Trim carrots and cut potatoes in half. Toss carrots and potatoes in olive oil and salt.

Spread on a parchment-lined baking sheet. Place in the middle rack of the oven to roast for 45 minutes or until fork tender.

Bring a large cast iron skillet to a medium high heat, add 1 tablespoon olive oil to coat the bottom, and a splash of curry sauce.

Once the pan is hot, sear duck breasts on all sides.

When the roasted vegetables have about 20 minutes left, add 1 cup pork broth to the duck breasts in the large skillet and place in oven, next to the vegetables.

Let the duck breasts cook in the oven for 15 minutes and then remove from the heat and let them rest for 5 minutes, while the vegetables finish.

Serve the braised duck breasts with the roasted vegetables and drizzle the curry sauce on top.