For the duck breast: Heat a medium saute pan over medium-high heat and add the oil.
Cut a crosshatch pattern into the skin of the duck breast, being careful to not cut through to the flesh. Season the skin side with the curry powder and the flesh side with some salt. Place in the pan, skin-side down. Cook, to render of some of the fat and crisp up the skin, 5 to 7 minutes. Flip, reduce the heat to medium, and cook on the flesh side for about 4 minutes for medium-rare. Remove from the pan and allow the meat to rest for 5 minutes.
For the pomegranate apple glaze: Make the sauce in the same pan used for the duck. (Wipe out the pan if you have burned bits on the bottom, and add some butter.) Place the pan over medium-high heat and add 1 tablespoon butter. Add the apple and onion and saute until onion is just translucent. Deglaze the pan with the pomegranate juice, then allow the juice to simmer and reduce by half. Turn off the heat and stir in the remaining 2 tablespoons butter. Taste and season with sugar if the sauce tastes too tart.
For the julienned vegetables: Heat a saute pan over medium heat and add some oil. Add the julienned vegetables and season to taste with salt and pepper. Cook, stirring occasionally, until the vegetables are just softened, 3 to 5 minutes.
Slice duck breast and serve with sauce on top and vegetables on the side.