Fill a medium pot with water, and add 2 garlic cloves, 1 onion cut in quarters, bay leaf, and salt. Bring to a boil and add the chicken breasts. Boil for 15-20 minutes or until cooked.
Let the chicken rest for 5 minutes. Place it in a deep bowl and use a hand mixer on low speed to break the chicken into shreds.
Cut the onion into thin rounds and mince 2 garlic cloves. Heat olive oil in a large saucepan on medium heat and cook onions for about 3 minutes. Season with salt, add minced garlic and oregano and cook for 2-3 minutes until golden.
Blend roasted tomatoes, chipotle, and an optional pinch of cinnamon in a blender until smooth. Pour into the pan, and add the shredded chicken. Season with salt (and sugar if needed), cover, and cook on low for 15 minutes.
Uncover and simmer for another 5 minutes. Add some leftover broth if the tinga is too dry. Your tinga de pollo is ready to serve!