Melt the butter in a large pot over medium heat. Add the onions, stir them to coat, then place a lid on the pot and leave for 5 minutes.
Take the lid off and stir the onions. Add the garlic and cover again until the onions are soft and just starting to brown, another 2 minutes.
Add the pureed tomatoes and vegetable broth to the pot and stir, being sure to scrape any sticky onions off the bottom to keep them from burning.
Bring the soup to a boil, then turn it down to a low simmer for about 10 minutes.
Taste and add salt and pepper as needed. For smooth soup, use an immersion blender to quickly puree the onions into the tomato mixture. If you're using a standard blender, wait for the soup to cool before you blend.
Notes
Recipe used with permission from Leanne Brown, author of "Good and Cheap: Eat Well on $4/Day."
Keyword 30 minutes or Less, Comfort Food, Vegetarian