Heat olive oil in a large pot or Dutch oven over medium heat. Add onion and garlic and sauté until translucent.
Add the beef chunks and sear until browned on all sides.
Add tomato paste, chilies, and spices. Stir to coat.
Pour in beef stock and add bay leaves. Bring to a boil, then reduce heat, cover, and simmer for 2.5 to 3 hours until the beef is fall-apart tender.
Remove the beef and shred it using two forks. Strain the broth and set it aside as consomé.
Dip a tortilla into the consomé, then place it on a hot skillet. Add shredded beef and cheese, then fold in half.
Cook until crispy on both sides. Repeat with remaining tortillas.
Serve with a small bowl of consomé for dipping. Garnish with onions, cilantro, and a squeeze of lime.