1. Preheat oven to 400°. Toss bread cubes with butter and 2 tablespoons olive oil; add sea salt and pepper. Spread cubes in a single layer on a rimmed baking sheet. Bake at 400° for 12 to 15 minutes or until golden brown.
2. Mix remaining olive oil and vinegar in a large bowl to blend. Toss in arugula, chicken, toasted bread, basil, and parsley. Divide evenly onto plates, and top with Parmesan cheese. Serve warm.