Step 1 Rinse the chicken bones with cold water and set aside.
Step 2 Heat the olive oil in a 4-quart stock pot set over medium-high heat. Stir in the onion, the celery and carrot and cook for 5 minutes, just until the onions are translucent, stirring occasionally. Lower the heat, if necessary, to keep the vegetables from caramelizing.
Step 3Stir in the turmeric, crushed dried limes and the mint and continue to saute for an additional 2 minutes.
Step 4Stir in the chicken back bones and add 2 quarts and 2 cups water (the water should cover the bones by about 3 inches). Bring the soup to a boil over high heat, and skim the fat and debris from the surface. Reduce the heat to a gentle simmer, and cook for 1 1/2 hours.
Step 5While the soup is cooking, make the dumplings: In a medium bowl, mix the ground chicken thigh meat with the garlic, Spanish onion, cardamom, matzo cake flour and 1 1/2 teaspoons salt. Roll the mixture into 1-inch meatballs, then flatten slightly into ovals and set aside on a parchment-lined baking sheet. Cover the sheet with plastic wrap and refrigerate until needed. This makes about 2 dozen meatballs.
Step 6Strain the soup into a clean pot, discarding everything but the broth. Bring the broth back to a simmer and gently add the chicken dumplings, one or two at a time. Cover and simmer for about 15 minutes, until the dumplings are cooked thoroughly. Season with 2 teaspoons salt, or to taste.
Step 7To serve, place a couple of dumplings into each soup bowl along with a few spinach leaves (and a few peas, if using). Add the fresh lime juice to the soup, and then ladle about 1 cup into each bowl. Serve immediately.