Pour the olive oil in a large soup pot turned to medium-high heat, and add in the onion, garlic, carrots, celery, and mushrooms. Cook, stirring occasionally, until vegetables are fragrant and slightly soft, 4-5 minutes.
Add in the chicken drumsticks and let them cook for a little bit.
Once the chicken has a nice sear, add the chicken broth, dry mushrooms, and all of the herbs and spices. Turn heat onto low, and let the soup simmer for at least 1 hour, until it has thickened and all vegetables are very soft.
After about 30 minutes, pull the chicken drumsticks out of the soup, clean all the meat off the bones, and add it back in.
When almost ready to serve, add in the pasta, along with about 1-2 cups extra water, and turn the heat on high.
Let the soup boil for 7-8 minutes, pasta is cooked through. Taste and add salt and pepper as needed, and serve immediately!