Glazed Winter Vegetable Medley With Chestnuts and Caper Berries From Feast

Name: Glazed Winter Vegetable Medley With Chestnuts and Caper Berries From 'Feast'
Ingredients: 12 fingerling potatoes, halved lengthwise; 4 tablespoons (60 ml) extra-virgin olive oil; Sea salt and freshly ground pepper; 1/2 head cauliflower, cut into large florets; 4 large shallots, quartered; 6 tablespoons (85 g) unsalted butter; 1 bunch golden beets, peeled and cut into bite-size pieces; 1 bunch baby turnips, scrubbed and trimmed; 1 bunch carrots, peeled and cut into bite-size pieces on the diagonal; 2 parsnips, peeled, cored, and cut into bite-size pieces on the diagonal; 3 sprigs fresh thyme; 1 to 1 1/2 cups (240 to 360 ml) vegetable stock or water; 1/2 teaspoon unbleached raw sugar; 5 oz (140 g) roasted peeled chestnuts (see Note); Handful fresh parsley, finely chopped; Finishing oil for drizzling; Fleur de sel or sel gris; Handful caper berries; Oil-cured black olives or kalamata olives for topping