Preheat oven to 425°F.
In a mixing bowl, combine tomatoes, olive oil, cumin seeds, light brown sugar, garlic, thyme, oregano sprigs, lemon strips, ½ teaspoon flaky salt, and a grind of pepper. Mix well to coat.
Transfer the tomatoes tightly packed to a baking sheet. Place the sheet 2-3 inches below the broiler and roast for 20 minutes, until tomatoes blister and juices bubble.
Switch oven to broil and broil for 6-8 minutes until the tops of tomatoes start to blacken.
Meanwhile, mix Greek yogurt with lemon zest and ¼ teaspoon flaky salt. Chill until ready to serve.
To serve, spread the lemon yogurt on a platter or shallow bowl. Spoon the hot tomatoes with their juices, lemon strips, garlic, and herbs on top. Garnish with oregano leaves and urfa chili. Serve immediately.