Chicken Soup with Parmesan Dumplings

Name: Chicken Soup with Parmesan Dumplings
Ingredients: 2 tbsp. extra-virgin olive oil; 2 medium carrots, peeled and thinly sliced; 2 celery stalks, thinly sliced; 1 small onion, diced; 2 cloves garlic, minced; kosher salt; Freshly ground black pepper; 2 qt. organic chicken stock, homemade or store-bought; 4 sprigs fresh thyme, plus 2 tsp. thyme leaves, divided; 1 c. all-purpose flour; 1/4 c. freshly grated Parmesan, plus more for serving; 1/2 c. whole milk; 1 large egg, beaten; 1 1/2 c. rotisserie chicken, shredded; 5 oz. baby spinach