Start the broth: Set a large Dutch oven or soup pot over medium heat.

Start the broth: Add the olive oil to the pot.

Start the broth: Add the chopped onion and 1/2 teaspoon of the salt to the pot. Cook for 5 to 6 minutes, stirring often, until the onion is soft and lightly golden at the edges.

Start the broth: Add the sliced garlic and chopped chipotle peppers to the pot. Cook for 30 seconds, stirring, until fragrant.

Build the soup: Pour the crushed tomatoes into the pot. Cook for 2 to 3 minutes, stirring often, until the tomatoes look slightly darker and thicker around the edges.

Build the soup: Pour the chicken broth into the pot. Scrape the bottom of the pot with a wooden spoon so any stuck tomato mixture loosens into the broth.

Build the soup: Add the drained hominy to the pot and raise the heat to medium-high.

Build the soup: Bring the soup to a full boil.

Let it simmer: Lower the heat to keep the soup at a gentle simmer. Cook for 10 minutes so the broth takes on the chipotle and tomato flavor.

Finish the soup: Add the shredded chicken to the pot.

Finish the soup: Simmer for 4 to 5 minutes, stirring once or twice, until the chicken is hot all the way through.

Finish the soup: Taste the broth and add the remaining 1/2 teaspoon salt, or more if needed, until the soup tastes well seasoned.