Combine the parsnips, milk and a large pinch of salt in a medium saucepan. Cover and bring to a simmer, then reduce the heat to low and cook, stirring occasionally, until tender, about 20 minutes. Transfer the mixture to a blender or food processor, add the butter and puree. Season with salt and pepper.
Meanwhile, heat 2 tablespoons vegetable oil in a large nonstick skillet over high heat. Season the scallops with salt and pepper, add to the skillet and cook, undisturbed, until well browned, about 3 minutes. Flip and cook through, about 1 more minute. Divide among plates.
Add the remaining 1 teaspoon vegetable oil and the hazelnuts and thyme to the skillet. Cook, stirring and scraping up the pan, until the nuts are toasted, about 1 minute. Scrape the mixture into a bowl.
Return the skillet to the heat and stir in the honey and 1/4 cup vinegar. Cook, swirling the pan, until thick, about 1 minute.
Thinly slice the shallot and put in a large bowl with the remaining 1 tablespoon vinegar, 1/4 teaspoon salt and a few grinds of pepper. Add the watercress and toss. Add the watercress salad and parsnip puree to the plates. Sprinkle with the hazelnut mixture and drizzle with the honey syrup.