Heat the olive oil in a large pot over medium heat. Add the diced onion and cook, stirring occasionally, until translucent and fragrant, about 5 minutes.
Add the minced garlic and chopped rosemary to the pot. Cook for another minute until the garlic is fragrant but not browned.
Pour in the white wine, scraping the bottom of the pot to lift any flavorful bits. Let it simmer for 2-3 minutes until the wine reduces slightly.
Add the chicken broth to the pot and bring the mixture to a gentle boil over high heat.
Meanwhile, cook the chicken breasts in boiling water until fully cooked, about 12-15 minutes. Remove and shred the chicken into bite-sized pieces.
Add the shredded chicken to the simmering broth, stirring to combine. Season with salt and pepper to taste.
Once the broth is bubbling, add the egg noodles and cook according to package instructions, about 8 minutes, until al dente.
Stir the soup occasionally to prevent sticking and to ensure even cooking. Adjust seasoning as needed.
Check the noodles for doneness, ensuring they’re tender but not mushy. The broth should be flavorful with a fragrant herbal aroma.
Serve the soup hot, garnished with a sprig of rosemary or a drizzle of olive oil if desired, for a warm, comforting meal.
