How to Make It
Preheat the oven to 375°. On a large rimmed baking sheet, toss the sunchokes with the olive oil and thyme sprigs and season with salt and pepper. Bake for about 25 minutes, stirring halfway through, until crisp-tender. Let cool completely. Discard the thyme sprigs.
Meanwhile, in a medium saucepan, cover the olives with water and bring to a boil, then drain the olives. Repeat this blanching step 2 more times. Return the olives to the saucepan. Add the red wine vinegar and the agave and bring just to a boil. Simmer over moderately low heat, stirring occasionally, until the olives are softened, 5 to 7 minutes. Transfer the olives and any liquid to a food processor and puree until smooth. Scrape the puree into a small bowl and season with salt and pepper; let cool completely.
In a small saucepan, cook the sugar with 1/2 teaspoon of water over moderate heat until golden, about 3 minutes. Remove from the heat and carefully add the Chardonnay vinegar. Cook over moderate heat until the caramel is dissolved, about 1 minute. Stir in the apple and cook until hot, about 2 minutes. Remove from the heat and stir in the sunflower seeds and 2 tablespoons of the chives. Season the relish with salt and pepper and let cool.
In a large bowl, whisk the buttermilk with the crème fraîche and walnut oil and season with salt and pepper. Add the cooled sunchokes and the remaining 2 tablespoons of chives and season with salt and pepper. Toss the salad gently. To serve, spread some of the olive puree on 6 plates and arrange the watercress on top. Spoon the dressed sunchokes over the watercress and top with some of the apple relish.