Preheat your oven to 400°F; place the corn tortillas on a baking sheet and bake for 4-5 minutes per side until they are crisp and golden brown.
In a large skillet, heat the extra virgin olive oil over medium heat, then add the diced white onion and sauté until soft and translucent.
Stir in the minced garlic, tomato puree, chipotle peppers, oregano, sea salt, and black pepper, allowing the sauce to simmer for about 5 minutes to develop flavor.
Fold the shredded chicken breast into the skillet, tossing thoroughly to ensure every piece is coated in the smoky sauce, and cook until the chicken is heated through.
To assemble, place the toasted corn tortillas on plates and divide the warm chicken tinga mixture evenly among the shells.
Top each tostada with a generous layer of shredded romaine lettuce, sliced radishes, a sprinkle of crumbled Cotija cheese, and a bright squeeze of fresh lime juice.