Preheat oven to 350°F. Toss together beets, thyme sprigs, 3 tablespoons olive oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a roasting pan or baking dish; cover tightly with aluminum foil. Bake in preheated oven until beets are tender, about 1 hour and 15 minutes. Remove foil, and let stand until cool enough to handle. Peel cooled beets, and cut into wedges. Discard thyme sprigs.
Heat 1 tablespoon grapeseed oil in a large cast-iron skillet over high until smoking. Add half of the haricots verts in an even layer. Cook, without stirring, until charred on one side, about 2 minutes. Cook, stirring often, until tender-crisp, about 3 minutes. Transfer to a plate. Repeat process with 1 tablespoon grapeseed oil and remaining haricots verts. Sprinkle beans with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Toss together beets, haricots verts, vinegar, sugar, mustard, oregano, chopped thyme, and remaining 2 tablespoons olive oil. Season with remaining 1 1/2 teaspoons salt and remaining 1/2 teaspoon pepper. Cover and refrigerate at least 2 hours or up to 2 days.
Stir together shallots and remaining 1/2 cup grapeseed oil in a small saucepan. Cook over medium-high, stirring occasionally, until golden brown and crisp, about 15 minutes. Using a slotted spoon, transfer fried shallots to paper towels to drain. Top salad with fried shallots; garnish with hazelnuts and parsley.