How to Make It
Preheat the oven to 400°. Put the beets in a small roasting pan and add 1/4 inch of water and salt. Tightly cover the pan with foil and bake the beets for 1 hour, or until tender. Drain and let cool, then peel the beets and slice them 1/4 inch thick. In the roasting pan, toss the beets with 1 tablespoon each of the olive oil and vinegar. Season with salt and pepper.
Meanwhile, in a small saucepan, cover the eggs with cold water and bring to a gentle boil. Reduce the heat to low and simmer for 8 minutes. Pour off the hot water and shake the eggs against the sides of the pan to crack the shells. Cover the eggs with cold water; let them soak for 5 minutes, then pat dry, peel and finely chop.
In a large saucepan of salted boiling water, cook the cauliflower until just tender, about 3 minutes. Drain well. Transfer the florets to a large bowl and toss with 1 tablespoon of the olive oil and the lemon juice. Season with salt and pepper.
In a medium bowl, soak the sliced shallot in the remaining 2 tablespoons of vinegar for 5 minutes. Add the parsley, mint and the remaining 5 tablespoons of olive oil. Fold in the chopped eggs and season with salt and pepper. Arrange the sliced beets on a large platter and scatter the cauliflower florets over them. Spoon the dressing over the salad and serve.
It is easiest to peel roasted beets with your hands while they are still slightly warm. Under cold running water, simply rub off the skins with your fingers. Slice the beets on a nonporous surface to avoid staining.