Bring a pot of water to a boil; add half an onion, 2 whole garlic cloves and the thyme. Cook chicken breast, bone and skin included.
Remove the chicken once cooked through after 20-30 minutes. Discard the onion, herbs and garlic, but set aside one cup of chicken stock.
Shred the chicken and set it aside.
In a frying pan, add a tablespoon of cooking oil and sauté half an onion coarsely chopped and two garlic cloves until fragrant and caramelized. Add the tomatoes cut into wedges and cook for 2-3 more minutes. Set aside.
Add to a blender one cup of chicken stock, the mole La Costeña and the stir-fried tomatoes, onion and garlic. Blend until smooth.
Heat the tortillas in a skillet until soft, and fill each with 2-3 tablespoons of shredded chicken.
Place the filled tortillas in a baking tray and top them with the mole.
Top with the grated cheese and serve immediately.
