Preheat the oven to 450°F. Spray a 13x9-inch baking pan with nonstick cooking spray.
Combine 1/2 cup of the broth, sugar, vinegar, and soy sauce in measuring cup or small bowl. Place the onion, garlic, and drained tomatoes in the prepared pan. Pour brother mixture over tomatoes and toss to combine. Bake for about 45 minutes, or until the vegetables are lightly browned.
Remove the tomato mixture to a large pot set over low heat. Add the remaining 1/2 cup broth and the half-and-half to the pot. Using an immersion blender, blend the mixture until desired consistency. Strain the soup, if a smoother texture is desired. Let mixture come to a gentle simmer then remove from heat. Season with salt and pepper if necessary before dividing between 4 bowls to serve. Garnish with chives.