Heat the olive oil in a large pot over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
In a small skillet, lightly toast the guajillo and ancho chiles over medium heat for about 1-2 minutes until fragrant. Be careful not to burn them. Transfer the chiles to a blender and add the cumin, oregano, smoked paprika, salt, black pepper, and 1 cup of chicken broth. Blend until smooth.
Add the chicken thighs to the pot with the sautéed onions and garlic. Pour the blended chile mixture over the chicken, then add the remaining chicken broth and bay leaves. Bring to a boil, then reduce the heat to low and cover. Simmer for about 1 hour, or until the chicken is tender and easily shredded.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the pot and stir to combine with the broth. Let it simmer for an additional 10 minutes to absorb the flavors.
To assemble the tacos, heat the corn tortillas in a dry skillet over medium heat until warm. Fill each tortilla with a generous amount of the chicken birria, then top with chopped cilantro and diced onion. Serve with lime wedges on the side for squeezing over the tacos.