Preheat oven to 400 degrees. Brush tortillas on both sides with 2 tablespoons canola oil; lay on a baking sheet. Bake until crisp and brown around edges, 7 to 10 minutes.
In bowl, beat eggs with salt and pepper. Heat remaining tablespoon oil in large skillet over medium-low heat. Cook eggs, stirring, until set but still moist, 6 to 8 minutes.
Place tortillas on plates; top with eggs, sauce rancheros, and Monterey Jack. Garnish with avocado, sour cream, and cilantro.