Preheat the oven to 400 degrees F.
Set a large saute pan over medium heat. Season the duck breasts with 1 teaspoon of salt, and 1/2 teaspoon of black pepper. Lay the duck breasts skin-side down in the hot saute pan and sear until golden brown and most of the fat had rendered from the skin, about 8 minutes. Pour off the excess fat from the pan, and turn the breasts over. Continue to cook the breasts on the flesh side for another 8 minutes. Remove the pan from the heat and place in the oven. Cook for 5 minutes, and remove to cool before slicing. Slice the duck thinly using an electric knife or a carving knife.
Heat the olive oil over a medium-high heat in a 10-inch saute pan. Once the oil is hot, add the shallots and garlic to the pan. Sweat, stirring continuously, for 1 minute. Add the blackberries to the pan and cook for 2 minutes. Deglaze the pan with the white balsamic and regular balsamic vinegars and allow it to reduce by half, about 30 seconds. Remove the pan from the heat and place the contents in a bar blender with the sugar, mint and tarragon. Pulse the berries in the blender until a smooth paste forms. With the machine running, season the berries with the salt and pepper and drizzle the light olive oil into the blender.
Once blended, strain the vinaigrette through a fine mesh sieve and allow it to cool completely before using, about 1 hour under refrigeration.
To assemble the salad, place the arugula, radicchio, walnuts, apples and goat cheese in a large mixing bowl with the endive spears. Toss the greens with the vinaigrette, season with salt and fresh ground black pepper. Divide the salad between 4 plates, and fan 1/2 a duck breast over each of the 4 plates.
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