Place pear halves, cut side down, in an 8x8x2-inch baking pan. Add the 3 tablespoons vinegar and 2 tablespoons water. Cover and bake in a 350 degree F oven for 15 to 25 minutes or until tender (baking time depends on ripeness of pears). Remove from oven; set pan on wire rack and uncover; let pears cool in liquid. When cool, lift pears from liquid; discard liquid. Place pears on a cutting board. Slice pears lengthwise from bottom up to, but not through, stem end; set aside.
Meanwhile, place walnuts on a baking sheet. Bake in a 350 degree F oven for 6 to 8 minutes or until light golden. Cool.
Stir together olive oil, the 1 tablespoon vinegar, shallot or green onion, garlic, salt, and pepper in a large bowl. Add greens; toss to coat. Arrange greens on two salad plates. Sprinkle with nuts. Fan a pear half atop each salad. Makes 2 servings.