To toast the chile: Place the chile 1- to 2-inches above an open flame for a few seconds, or until fragrant, turning frequently or place the chile in a dry pan over medium heat, pressing the chile flat and turning once. Break the toasted chile into pieces and put in a blender along with the tomatoes with their juice.
Cook's Note: A food processor will work, though it won't completely puree the chile.
To make the soup: In a medium saucepan (about 3- to 4-quart) over medium-high heat, add oil and heat 1 minute. Add the onion and garlic and cook, stirring frequently, until golden, about 7 minutes. Using a slotted spoon, remove the onion and garlic pressing the mixture against the side of the pan to leave behind as much oil as possible, and transfer onion-garlic mixture to the blender. Blend until smooth.
Increase the heat under the saucepan to medium-high for 1 minute. Add the onion puree and stir constantly, until thickened to the consistency of tomato paste, about 6 minutes. Add the chicken broth and epazote sprig. Reduce the heat to medium-low and simmer 15 minutes. Taste and season the soup with salt, usually about a generous teaspoon (depending on the saltiness of the broth).
Just before serving, add the chicken to the simmering broth. Divide the avocado, cheese and tortilla chips among 6 serving bowls. When the chicken is cooked through, about 5 minutes, ladle the soup into the bowls.
*Can be found at Mexican specialty markets. A note about pasilla (sometimes called negro) chile: Its unique flavor defines tortilla soup in central Mexico. In Michoacan, it's ancho chile. In your kitchen, it might turn out to be another chile, like New Mexico or even a little smoky chipotle (be forewarned that chipotle will make the broth quite spicy). Though for these everyday recipes I've relied heavily on the easier-to-use powdered dried chile, finding powdered pasilla (negro) can be harder than finding the whole pod. Should powdered chile be at your finger tips (be it powdered pasilla (negro), ancho or beyond), add about 1 tablespoon to the pan about halfway through the cooking of the onion. In Mexico, it's more common to crush toasted chile pods over the soup than to add it to the base. You can follow that lead, or do both as we do in our restaurants. Vegetarian tortilla soup: Use vegetable broth instead of chicken broth and omit the chicken. Or replace the chicken with 1/2-inch cubes of firm tofu (I like to cut half-inch slices, sear them in my grill pan, and then cut them into cubes before adding to the soup). Tortilla soup with greens: Add a couple handfuls of sliced chard leaves (or practically any other green) to the soup along with the chicken. Hearty greens like collards and kale should be added before the chicken; soft greens like spinach or arugula should go in when the chicken is half done. Contemporary riffs on the tortilla soup theme: Goat cheese can replace the melting cheese. Rotisserie or grilled chicken and grilled duck breast or confit-style legs may be substituted for raw chicken breast (add it at the last second). Blue corn tortilla chips are delicious, though perhaps not as pretty.