Preheat the oven to 400 degrees F.

Line a baking sheet with parchment paper and place the apricots, cut side up on the pan. Place a small piece of butter inside the cavity of each apricot and sprinkle with the sugar. Roast the apricots in the oven until they become golden brown on top and begin to feel soft, about 20 minutes.

In the bowl of a food processor combine the toasted pistachios, melted butter, shallot, garlic and lemon zest and process until almost smooth. In a medium saucepan heat the heavy cream until almost simmering. Add the pistachio mixture to the heavy cream and continue to simmer for 8 to 10 minutes or until the cream begins to thicken slightly. Add the tarragon and season, to taste, with salt and pepper.

Season the entire duck breast with salt and pepper. In a large saute pan, over medium heat, add the olive oil. When the oil is hot, add the duck breast, skin side down. Sear for 6 minutes. Flip the duck breast over and place the pan in the oven. Roast the breasts for 5 to 7 minutes for medium rare. Remove the pan from the oven and allow the duck breasts to rest 2 to 3 minutes before slicing. Slice each duck breast, on the bias, into 1/2-inch pieces.

Serve the sliced duck breasts with the roasted apricots and pistachio cream sauce. Serve immediately.