In a large Dutch oven, heat the olive oil over medium-high heat. Add the minced garlic and sauté for 30 seconds until fragrant.
Next, stir in the chopped onions, cover, and cook for about 10 minutes, stirring occasionally. Once the onions start to soften, uncover the pot and continue cooking, stirring often, for an additional 5-10 minutes until the onions are a rich caramel color.
Now it’s time to add the tomatoes and spices. Stir in the diced tomatoes, broth, brown sugar, chili powder, salt, cumin, ground red pepper, and the softened chiles, along with the reserved soaking liquid. Once everything is well combined, remove the pot from the heat and let the flavors meld for a minute or two.
Transfer the mixture in batches to a blender and blend until smooth (you can also use an immersion blender directly in the pot). Return the pureed soup to the Dutch oven.
Bring it to a boil over medium-high heat, then reduce the heat to low and let the soup simmer uncovered for 15 to 20 minutes. Stir occasionally, and as the soup simmers, it will thicken and darken in color. (Stop when it's as thick as you like your soup. You should have about 9 to 10 pints.)