In a large saucepan over medium heat, add the oil and heat until shimmering. Add the onions and cook, stirring often, for 5 minutes or until the onions are translucent. Add the garlic and cook, stirring, for 1 minute or until fragrant. Add the chipotle peppers and cook, stirring, 1 minute or until peppers are lightly toasted. Stir in the adobo sauce, tomatoes, chicken broth, oregano, cumin, and ½ teaspoon kosher salt. Heat until simmering and cook, stirring frequently, for 7 minutes or until the flavors are melded. Reduce heat to low.
Using and immersion blender, blend tomato mixture until smooth. Add a pinch of sugar, if needed for sweetness.
Add the chicken to the sauce and cook, stirring often, for 5 to 7 minutes or until chicken is heated through and coated with sauce. Season to taste with salt.
Meanwhile, in a cast iron skillet over medium-high heat, add a tortilla and cook, 15 to 30 seconds per side or until they smell toasty and have a few darkened spots. Transfer to a plate and repeat with remaining tortillas.
Spoon chicken tinga onto each tortilla. Serve garnished with red onions, cilantro, cotija, and lime wedges.