Cook the onion and bell pepper in the oil in a large, heavy-bottomed pot over medium heat for about 5 minutes, stirring as they soften. The onion should turn translucent and the pepper should lose its raw firmness.

Distribute the cumin, chili powder, and kosher salt over the vegetables, then stir and cook for about 2 minutes. The warm oil should bring out a noticeably earthy, toasted spice aroma without scorching the seasoning.

Combine the enchilada sauce, chicken broth, salsa, and chicken breast in the pot, bring the mixture to a boil, then simmer uncovered for 30-40 minutes. Check the thickest part of the chicken for an internal temperature of 165 °F, since thicker pieces may need more time within that range.

Lift the cooked chicken out with tongs and place it on a cutting board, then shred or cut it into bite-sized pieces once it's comfortable to handle. For shredded chicken, the meat should pull apart readily into strands.

Reduce the heat to gentle warmth and gradually stir the sour cream and shredded cheddar into the broth. Continue stirring until the dairy blends in and the broth looks creamy rather than streaked with cheese.

Fold the chicken, cilantro, and green onions into the finished broth. The chicken should distribute evenly, with fresh green flecks throughout the soup.