Trim beets, leaving roots and 1" stems. Scrub beets with a vegetable brush. Place beets in a medium saucepan; add water to cover. Bring to a boil; cover, reduce heat, and simmer 35 to 40 minutes or until tender. Drain; rinse with cold water, and drain again. Trim stems and roots, and rub off skins. Cut beets into 1" pieces.
Combine minced shallot and next 4 ingredients in a large bowl. Add beets; toss. Cover and chill 1 hour.
Melt butter in a skillet over medium heat. Add curry powder, sugar, and 1/4 teaspoon salt; cook 1 minute. Add walnuts, and cook, stirring constantly, 2 minutes.
Toss greens in olive oil; divide among 6 plates. Top with beet salad and curried walnuts.