Best-Ever Avgolemono Soup

In a large pot over medium heat, heat oil. Add onion, carrots, and celery and cook until soft, 5 minutes. Add garlic and cook until fragrant, 1 minute more. Add broth, thyme, and oregano and season with salt and pepper. Bring to a boil. Add rice and reduce heat to a simmer. Simmer until rice is cooked through, 20 minutes. Add chicken to pot and bring back to a simmer. In a medium bowl, whisk together egg yolks and lemon juice. Slowly add ¼ cup of hot broth to eggs while whisking. Slowly whisk mixture back into the pot. Let simmer until thickened, 5 minutes.  Serve soup with fresh dill and lemon wedges.