Cut tortillas into 1-inch-wide strips. Pour oil into a 5- to 6-quart pan over high heat. When oil is hot, add tortilla strips and stir often until crisp and lightly browned, 2 to 3 minutes. Transfer tortilla strips to towels to drain.
Add onion and garlic to pan. Stir often over medium-high heat until onion is limp, 3 to 4 minutes. Add bay leaf, oregano, peppercorns, chili flakes, and broth. Bring to a boil over high heat and boil until reduced to about 6 cups, 20 to 25 minutes.
Prepare Salsa Fresca while soup boils: Rinse and core tomatoes and cut into about 1/4-inch dice; put the tomatoes with their juices into a bowl. Rinse and stem the jalapeño; shake out seeds and cut out the veins. Finely chop the chili. Add it to the bowl, along with the onion, cilantro, and 3 tablespoons lime juice. Stir gently to mix, and add more lime juice and salt and pepper to taste.
Coarsely puree half the salsa fresca in a blender. Pit, peel, and thinly slice the avocado. Cut lime crosswise into thin slices; discard ends.
In wide soup bowls (at least 1 1/2-cup size), arrange equal portions of tortilla strips, remaining salsa, avocado slices, lime slices, and jack cheese.
Pour puréed salsa into hot soup, season to taste with salt and pepper, and ladle over condiments into prepared bowls.