Preheat the oven to 450 degrees F and place the whole beets in a baking dish. Roast for 1 hour, until soft. Cool completely, then peel and slice into 1/8-inch rounds.
Preheat the oven to 300 degrees F. Slice the tomatoes into 1/3-inch rounds and lay out on foil-lined rimmed baking sheets. Drizzle with olive oil and salt and pepper liberally. Place in the oven and roast for 75-90 minutes, until the tomatoes are soft and wrinkled. (If you have 2 ovens, roast both the beets and the tomatoes at the same time.)
Shave the carrots into thin ribbons with a veggie peeler and shave the red cabbage into a thin slaw. Peel and slice the avocados into thin pieces.
Arrange all the vegetables into rows on a large platter. Then pour all the ingredients for the vinaigrette in a small bowl and whisk. Salt and pepper to taste.
Drizzle the pesto vinaigrette over the roasted rainbow salad and serve immediately.