Preheat the oven to 400F. Lightly scrub and thoroughly rinse the beets under cold water to remove any surface dirt. Trim the stems. Wrap the beets in aluminum foil, completely enclosing them. If you use different varieties of beets, wrap each separately to prevent the colors from bleeding. Put the wrapped beets on a large nonstick baking sheet. Bake for 40 minutes.
Meanwhile, cut the bell pepper in half. Remove the stem, ribs, and seeds. Cut each half into 2-inch squares. Peel the shallots and cut in half. Unwrap the beets and return to the baking sheet. Arrange the bell pepper and shallots in a single layer on the baking sheet, leaving room for the asparagus and walnuts to be added later. Lightly spray the foods with vegetable oil spray.
Bake, uncovered, for 20 minutes. Arrange the asparagus and walnut halves in a single layer on the baking sheet. Lightly spray the foods with vegetable oil spray.
Bake, uncovered, for 10 minutes, or until the beets are tender when pierced with a sharp knife, the other vegetables are tender, and the walnuts are a light golden brown. Put the baking sheet on a cooling rack and let cool for 10 minutes.
In a small bowl, whisk together the dressing ingredients. When the beets are cool enough to handle, peel and cut into quarters. Arrange the roasted vegetables on a serving platter. Arrange the walnut halves on top of the vegetables. Drizzle with the dressing. Serve warm or at room temperature.