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 ribs celery, thinly sliced; 1 small onion, diced; 2 cloves garlic, minced; kosher salt; Black pepper; 2 quarts 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. grated Parmesan, plus more for serving; 1/2 c. milk; 1 large egg, beaten; 1 1/2 c. shredded rotisserie chicken; 5 oz. baby spinach (about 5 cups)