Heat oven to 450°F. Place tomatoes cut-side up on a rimmed sheet. Brush with 1 tablespoon oil; season with 1/2 teaspoon salt and pepper. Roast 25–30 minutes until soft and browned-edged. Chop; reserve juices.
Meanwhile, heat remaining oil in a soup pot over medium. Cook turkey and onion 8–10 minutes, breaking up turkey, until it reaches 165°F on a thermometer. Stir in garlic for 30 seconds.
Add turnips, carrots, broth, thyme and remaining salt. Bring to a simmer; cook 8 minutes.
Add cauliflower and roasted tomatoes with juices. Simmer 10–12 minutes until vegetables are tender.
Add spinach; cook 2 minutes until wilted. Remove from heat; stir in vinegar.