Rinse, core, and cut tomatoes in half crosswise.

Fit tomatoes, cut sides up, in 10- by 15-inch pans (you'll need 3, or use 1 pan and refill). Brush the tops of the tomatoes in each pan with 1 tablespoon oil and sprinkle with 1 teaspoon sugar.

One pan at a time, broil tomatoes 3 to 4 inches from heat until tops are spotted black, about 20 minutes. Adjust pan position for even heat and remove tomatoes as they are charred.

Meanwhile, in an 8- to 10-quart pan over medium-high heat, combine remaining oil, garlic, and onions. Stir often until onions are lightly browned and taste sweet, 10 to 15 minutes.

In batches, smoothly purée tomatoes and onion mixture in a blender or food processor. To remove skins, if desired, rub tomato mixture through a fine strainer into a large bowl.

Return tomato mixture to pan and add broth; heat to simmering, stirring. Add salt to taste. To serve cold, cover and refrigerate until chilled. To store, cover airtight and chill up to 3 days, or put in freezer containers in easy-to-use portions and freeze up to 1 year.