Southwestern Wedding Soup

Name: Southwestern Wedding Soup
Ingredients: 1 large egg; 1/4 c. crushed tortilla chips; 1/4 c. finely grated cotija or Parmesan; 1 lb. ground pork; 3 garlic cloves, minced; 2 tbsp. finely chopped fresh cilantro; 1 tsp. chili powder; 1 tsp. kosher salt; 1/2 tsp. dried oregano; 1/2 tsp. freshly ground black pepper; 1/2 tsp. ground cumin; Vegetable oil, for greasing; 1 tbsp. vegetable oil; 1 medium yellow onion, finely chopped; 1 medium carrot, finely chopped; 2 celery ribs, finely chopped; 2 garlic cloves, minced; 2 tbsp. tomato paste; 1 (4-oz.) can diced green chiles; 2 tbsp. adobo sauce from a can of chipotle chiles; 8 c. low-sodium chicken broth; 1/2 c. acini di pepe or other small pasta shape; 5 oz. baby spinach; 1/4 c. finely chopped fresh cilantro; Kosher salt; Freshly ground black pepper; Crumbled cotija or finely grated Parmesan and lime wedges, for serving