Place a stockpot over medium heat and coat with 2 tablespoons of the olive oil.
Add the onions, garlic, jalapenos, and tomatoes; cook, stirring for 15 minutes until the vegetables are cooked down and pulpy.
Pour in the stock, season with salt and pepper, and simmer for 20 minutes.
Meanwhile, heat 1-inch of canola oil in a skillet over medium-high flame.
When the oil begins to smoke, add the tortilla strips in batches and fry until they are crisp on all sides.
Remove to a paper towel-lined platter and sprinkle with salt while they are still hot.
Ladle the hot soup into 4 soup bowls and put a pile of shredded chicken on top of each.
Top with the diced avocado and fried tortilla strips (and cheese if using).
Garnish with cilantro and serve with lime wedges.