Preheat oven to 400°.
Combine first 3 ingredients; rub over pheasant beneath the skin (skin should be loose). Place breast, skin side up, on a broiler pan coated with cooking spray. Lightly coat breast with cooking spray. Insert meat thermometer into meat, making sure not to touch bone; bake at 400° for 45 minutes or until thermometer registers 180°. Let stand 10 minutes. Discard skin; thinly slice breast, and set aside.
Combine salad greens and cabbage in a bowl. Combine vinegar, water, oil, 1/4 teaspoon salt, and 1/8 teaspoon pepper, stirring well with a whisk. Reserve 1 tablespoon vinaigrette; set aside. Pour remaining vinaigrette over greens mixture, tossing gently to coat. Arrange 2 cups greens mixture on each of 3 salad plates. Divide pheasant evenly among salads; sprinkle each with 1 tablespoon cranberries and 1 teaspoon hazelnuts. Drizzle reserved vinaigrette over salads.
Note: To get a 1-pound pheasant breast, have your butcher portion a 2 1/4-pound pheasant; reserve remaining pieces for another use.