Cook beets in water to cover until tender, about 40 to 45 minutes. Drain the beets and set aside to cool.
For the dressing, whisk together olive oil, shallot, half the lemon juice, thyme, salt and pepper. Set aside. While the beets are cooling, wash the watercress and trim the thicker stems from the leaves. Spread the trimmed watercress over some paper towels to dry.
When the beets are cool enough to handle, use a paring knife to peel off the beets’ skins. Cut the beets into quarters lengthwise and then those pieces in half crosswise. Place the beets and watercress in separate bowls. Divide the dressing between the 2 bowls. Toss the watercress and beets until evenly coated with the dressing. Spread the watercress on a serving platter to make a bed for the beets. Crumble the cold cheese into the beets and toss gently. Spread the beets over the bed of watercress and sprinkle with remaining lemon juice. Serve immediately.