Preheat oven to 400 degrees F. Cut polenta into 1/4-inch slices, then cut each slice in half. Brush polenta with oil. Arrange in a single layer in a shallow baking pan. Bake about 15 minutes or until light brown, turning once.
Meanwhile, in a large skillet, cook sausage over medium heat for 5 minutes, turning to brown evenly. Remove sausage from skillet. Drain off fat; wipe skillet with paper towels.
Return sausage to skillet; add apple juice, balsamic vinegar, and dried tomatoes. Bring to boiling; reduce heat. Simmer, covered, for 8 to 10 minutes or until sausage is no longer pink (160 degrees F).
To serve, divide salad greens among four dinner plates. Arrange polenta slices and sausage pieces next to greens. Drizzle balsamic mixture over greens, polenta, and sausage. If desired, sprinkle with nuts. Makes 4 servings.