Step 1Remove the duck breasts from the refrigerator. Using a sharp knife, score the skin in a crisscross pattern without cutting into the meat. Season the breasts on each side with a pinch each of salt and pepper. Set aside.
Step 2In a small bowl, whisk together the shallots, thyme, rosemary, maple syrup, vinegar and olive oil. Season with one-half teaspoon salt and a grind of black pepper, or to taste. This makes about 1 cup vinaigrette.
Step 3In a large bowl, combine the lettuces. Toss the lettuces with enough vinaigrette to lightly coat, 4 to 5 tablespoons, more if desired. Set aside.
Step 4Heat a cast-iron pan over high heat until hot. Add the vegetable oil and then add the duck, skin-side up. Sear the breasts for about 2 mintues to give them some color. Flip the breasts over and reduce the heat to medium-high. Continue cooking until the skin is crisp and the breasts reach the desired doneness, 7 to 10 minutes. Remove from the pan and set aside to cool slightly.
Step 5Reduce the heat to medium. Drain all but 2 to 3 tablespoons fat from the pan, and add the apple, along with the brown sugar. Cook the wedges until slightly softened, 5 to 7 minutes. Increase the heat to medium high and continue to saute the apple until the sugar caramelizes and the wedges take on some color, an additional 2 to 3 minutes. Remove from heat.
Step 6Divide the apples and salad between 4 plates, crumbling the blue cheese over each salad. Slice the duck breasts on the bias, and divide the duck between the plates. Serve immediately.