For stock: Season chicken thighs well with salt and black pepper. In a large Dutch oven, heat 1 tablespoon olive oil over medium. Sear thighs skin sides down in hot oil until browned, about 6 minutes. Turn thighs and cook 4 minutes more. Transfer to a plate. Add the white ends of green onions (save the green tops for garnish), the cilantro stems (save the leaves for garnish), smashed garlic, coriander seeds and cumin seeds to pot; cook and stir until aromatic, 30 to 60 seconds. Add celery, carrots, coarsely chopped onion, and chopped jalapeño pepper. Return chicken to pot. Add 2 quarts water and 1 tablespoon salt. Bring to a boil, reduce heat, cover and simmer 2 hours. Remove chicken and set aside to cool. Strain stock and skim fat.
For soup: Return pot to stove. Heat 2 tablespoons olive oil over medium. Add 1 cup chopped onion, 1 teaspoon salt and 1/4 teaspoon black pepper; cook until tender and beginning to caramelize, 8 to 10 minutes. Add grated garlic; cook 1 minute more. Add the stock and tomatoes. Bring to a boil and simmer 10 minutes.
Use an immersion blender to puree soup, adding enough torn tortillas until soup reaches desired thickness. Add jicama and sliced carrots; return to a boil. Simmer until vegetables are tender, about 10 minutes; remove from heat. Add chicken, removed from bones and torn into pieces. Serve soup with desired garnishes.