In a large, heavy-bottomed Dutch oven (about 6 quarts), heat the olive oil over medium-high heat. Add the minced garlic and sauté for about 30 seconds, until fragrant.
Add the coarsely chopped onions. Cover and cook, stirring occasionally, for about 10 minutes until the onions begin to soften. Once softened, uncover and continue cooking, stirring often, for an additional 5-10 minutes, until the onions become a deep caramel color.
Stir in the diced tomatoes, brown sugar, chili powder, salt, cumin, ground red pepper, and the softened chiles (along with the reserved soaking liquid). Remove the pot from the heat and let everything blend together.
Working in batches, transfer the tomato mixture to a blender and blend until smooth. (Alternately, use an immersion blender.)
Pour the pureed sauce back into the Dutch oven and bring it to a boil over medium-high heat. Once boiling, reduce the heat and let the sauce simmer uncovered for about 25 minutes, stirring often. The sauce should thicken and darken in color as it cooks.