Place the chicken breasts in a 3-quart pot and add 8 cups of water along with 2 garlic cloves, one tablespoon of salt, peppercorns, and cilantro. Bring to a simmer, skimming off any foam that rises to the surface.
Poach the chicken until the meat is cooked through, about 15 minutes. Remove the chicken and set aside on a plate. Simmer the broth while you make the rest of the soup.
Chop the remaining 3 garlic cloves. Add the vegetable oil to another medium pot (a Dutch oven works well) over medium heat and add the oil. When the oil is warm, add the onion and garlic and cook, stirring, until tender and just turning golden, 5 to 7 minutes. Add the tomatoes and chipotles to the pot and stir to combine. Use an immersion blender or transfer mixture to a blender and puree until smooth.
Return pureed mixture to the pot over medium to medium heat, place the lid over the pot just barely off-center so some steam can escape, and cook, stirring occasionally, for about 6 minutes or until the mixture has thickened up a bit. The mixture will splatter so keeping the lid on is helpful. Add the stock, remaining teaspoon of salt, cumin, and optional oregano and stir to combine. Remove the lid, reduce heat to medium-low and simmer for about 15 minutes.
Shred or chop chicken meat and add it to the pot. Simmer for a few minutes to warm it through. Taste and adjust seasoning as needed. Serve the soup topped with tortilla chips and any additional garnishes you like.