Stack tortillas and cut 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. Remove from heat and, with a slotted spoon, 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.
Meanwhile, whirl half the salsa fresca in a blender until coarsely puréed. Pit, peel, and thinly slice the avocado. Rinse lime and cut 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 equally around tortilla strips and garnishes in bowls.