Toss pecans with 1 tablespoon olive oil, kosher salt and Tabasco. Place on a baking sheet and place sheet in a preheated 325 degree oven. Toast pecans until darker brown, but not burnt. Remove from oven and cool.
Heat 1/3 cup olive oil in a skillet over medium-high heat. Add mushrooms and garlic and saute for 3 –4 minutes. Mushrooms should still be a little firm. Stir in basil, mustard and sliced cooked duck. Heat to warm and blend ingredients.
For each serving, place an iceberg wedge on a plate. Spoon mushroom and duck mixture over. Top with cheese, onion and tomato. Drizzle any remaining dressing over.