Step 1

Preheat oven to 425°F. Toss together tomatoes, onion, garlic, thyme, oil, pepper, and 1⁄2 Tbsp. of the salt on a large rimmed baking sheet. Arrange tomatoes evenly, cut side down, on baking sheet. Bake in preheated oven until tomato skins begin to blister, 25 to 30 minutes.

Step 2

Peel and discard skins from cooked tomatoes; discard thyme from baking sheet. Transfer peeled tomatoes, onion, garlic, and any accumulated juices from baking sheet to a Dutch oven. Add broth, vinegar, and remaining 1⁄2 Tbsp. salt. Process mixture with an immersion blender until smooth, about 2 minutes. Bring to a simmer over medium; simmer 10 minutes.

Step 3

Remove from heat; stir in cheese until melted and smooth. (If soup is not completely smooth, process once more with immersion blender.) Spoon soup evenly into 6 bowls; sprinkle with additional cheese, pepper, and chives.