Heat olive oil in a large Dutch oven or heavy pot over medium heat. Add diced onion and cook until softened, about 5 minutes. Stir in minced garlic and cook for 30 seconds until fragrant.
Pour in chicken broth, then add bay leaves, thyme, and rosemary. Season with a pinch of salt and pepper. Nestle the chicken thighs into the liquid. Bring to a boil, then reduce heat to low, cover, and simmer for 20 minutes, or until chicken is cooked through and reaches 165°F internally.
Remove chicken thighs with tongs and place on a cutting board. Let cool slightly, then shred with two forks into bite-sized pieces. Set aside.
Add carrots, celery, potatoes, and green beans to the broth. Return to a gentle boil, then reduce heat and simmer, uncovered, for 10-15 minutes until vegetables are just tender but still have a slight bite.
Stir in corn and the shredded chicken. Simmer for an additional 5 minutes to heat everything through. Remove bay leaves. Taste and adjust seasoning with salt and pepper.
Ladle soup into bowls, top with fresh parsley, and serve immediately with crusty bread or crackers.