To make dressing, in food processor blend shallot, mustard, brown sugar and vinegar. Slowly drizzle in the canola oil until blended. Alternatively, you can finely chop one shallot and combine with mustard and brown sugar and vinegar. Whisk in canola oil. Add salt and pepper to taste.
Precook all vegetables except beets, which can be heated with some oil on a saut� pan over medium heat.
Put all vegetables in a large bowl and gently toss with dressing while warm.