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- Preheat oven to 350°. Toast walnuts on a rimmed baking sheet, tossing once, until slightly darkened in color and fragrant, 8–10 minutes. Let cool; coarsely chop.
- Whisk vinegar, lemon juice, shallot, and mustard in a medium bowl. Whisking constantly, gradually add oil. Whisk until emulsified; season vinaigrette with kosher salt and pepper. Stir in thyme.
- Toss watercress, radicchio, carrots, turnips, oranges, kumquats (if using), and toasted walnuts in a large bowl. Drizzle with vinaigrette, season with sea salt and pepper, and toss again to coat.