Preheat the oven to 375°F (190°C). Place the tortillas on a flat surface and brush both sides lightly with 1 tablespoon of oil. Cut each tortilla in half, then slice into ¼-inch-wide strips. Arrange the strips evenly on a baking sheet, sprinkle with salt, and bake for about 12 minutes, or until crisp and golden brown. Remove from the oven and let cool — these will be your crunchy topping.
In a large, heavy-bottomed skillet or saucepan, heat the remaining 1 teaspoon of oil over medium heat. Add the chopped onion and sauté for about 5 minutes, stirring occasionally, until it becomes soft and translucent. Stir in the minced garlic, jalapeño, cumin, and oregano, cooking for another minute to release their aromas.
Pour in the chicken broth and diced tomatoes with their juices, stirring to combine. Bring the mixture to a gentle boil, then lower the heat to a simmer. Let it cook uncovered for about 10 minutes, allowing the flavors to meld and the soup to slightly thicken. Stir in the fresh lime juice to brighten the flavor.
Remove the soup from the heat. Using an immersion blender, carefully puree the mixture until it becomes smoother and slightly lighter in color, leaving some tomato texture intact. If using a regular blender, work in two batches, blending briefly to maintain a rustic consistency.
Ladle the soup into bowls and top each serving with a handful of crisp tortilla strips, a dollop of sour cream, and a sprinkle of freshly chopped cilantro. Serve warm, letting each spoonful bring together smoky spices, tangy tomato, and the perfect crunch of baked tortilla.