Make a roux: Melt the butter in a large pot. Add the flour. Stir until combined and continue stirring until the mixture turns a golden color.
Slowly add the first cup of stock a little bit at a time whisking each addition until the mixture is smooth. Add three more cups of stock. Whisk until fully combined.
Add the roasted veggie mixture and stir until smooth.
Add the hominy, cumin, salt, and chicken. Bring to a boil and simmer for 5-10 minutes. Season with additional salt and pepper as needed.
To serve, squeeze some fresh lime juice into a bowl of soup and top with any desired toppings such as sour cream, cilantro, cotija cheese, or tortilla chips.