Preheat the oven to 425°F (220 ̊C).
Drizzle red and golden beets with olive oil, salt and pepper and tightly wrap, a few together at a time, but dividing by color, in foil with a few thyme sprigs. Place foil packets on a rimmed baking sheet and roast until the beets are tender when pierced with a knife, 45 minutes to 1 hour, depending on the size of your beets. Unwrap the beets and let them cool slightly. When beets are cool enough to handle, peel by gently rubbing skin under cold running water or gently peel off with your fingers.
While the beets are roasting, toast the hazelnuts on a rimmed baking sheet for 4-6 minutes, or until they’re golden and fragrant. Place the toasted nuts on a kitchen towel and rub them against one another to remove the skins (don’t worry if all of the skins don’t come off). Roughly chop the nuts.
Using a sharp knife, remove the pith and peel from the blood oranges, and slice them crosswise in ¼-inch-thick rounds.
Squeeze the juice from the end orange pieces into a bowl. Reserve 1 tablespoon of blood orange juice in a separate bowl. Add yogurt to the bowl with most the juice and whisk together with honey, cumin, and salt.
In the bowl with the remaining 1 tablespoon of blood orange juice, whisk together shallot, vinegar, and blood orange while drizzling in olive oil. Season with salt and pepper.
Cut the beets into wedges and toss them with some of the dressing, making sure to keep the golden and red beets in separate bowls.
Just before serving, slather the yogurt on a serving bowl or tray. Arrange the beets and blood orange slices over the yogurt, spooning some of the dressing over the top. Sprinkle with the chopped hazelnuts and a healthy dose of tarragon. Season to taste with salt and pepper.