Place the chicken breasts in a medium pot and cover with water. Bring to a boil over medium-high heat, then reduce heat and simmer for 15-20 minutes until the chicken is cooked through.
Remove the chicken from the pot and let it cool slightly. Shred the chicken using two forks and set aside.
Heat the vegetable oil in a large skillet over medium heat. Add the sliced onion and cook for 5 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the chopped tomatoes, chipotle peppers, adobo sauce, oregano, cumin, smoked paprika, salt, and black pepper to the skillet. Cook for 5 minutes, stirring occasionally, until the tomatoes break down.
Transfer the tomato and chipotle mixture to a blender or use an immersion blender and blend until smooth.
Return the sauce to the skillet and add the chicken broth. Bring to a simmer over medium heat.
Add the shredded chicken to the sauce and stir to combine. Simmer for 10 minutes, allowing the flavors to meld and the sauce to thicken slightly.
Taste and adjust seasoning if needed.
Serve the Chicken Tinga hot, garnished with fresh cilantro leaves.