Preheat oven to 450°F. Combine half of the olive oil (2 tablespoons), chili powder, cumin, and oregano in small bowl; stir until well blended and set aside. Line a jelly roll pan or cookie sheet with parchment paper. Spread tomatoes and onions in the pan in a single layer. Brush with the seasoned oil and roast for about 30 minutes, or until the tomatoes are soft and the onions have a few brown spots. Set aside to cool slightly.
Reduce oven temperature to 400°F and line another cookie sheet with parchment paper. In a large bowl, toss the tortilla strips with 1 tablespoon olive oil. Spread them in a single layer on the cookie sheet and bake 10 minutes, stirring once, until they are crisp and browned. You may need to let them go for an additional few minutes. If so, keep an eye on them as they will get overly brown very quickly. Remove from oven and let cool.
Make this recipe vegetarian by skipping the chicken and using vegetable broth instead of chicken stock. Make it vegan by skipping the cheese too.