Heat the olive oil: In a large Dutch oven, heat 2 tablespoons of olive oil over medium-high heat.
Cook the chicken: Season the diced chicken thighs with salt and black pepper, then add them to the Dutch oven. Cook for about 5-7 minutes, stirring occasionally, until the chicken is browned on all sides. Remove the chicken from the pot and set it aside.
Sauté the vegetables: In the same pot, add the onions, carrots, and celery. Cook for 5 minutes, or until the vegetables begin to soften. Stir in 2 tablespoons of flour and cook for another minute, allowing the flour to coat the vegetables.
Add the herbs and broth: Stir in the dried rosemary, thyme, sage, and a pinch of salt and pepper. Add the chicken broth, scraping up any browned bits from the bottom of the pot. Bring the mixture to a simmer.
Add potatoes and chicken: Add the diced potatoes and browned chicken back into the Dutch oven. Cover and simmer for 15-20 minutes, or until the potatoes are tender.
Add green beans, corn, and milk: Stir in the green beans, corn, and remaining 3 tablespoons of flour, followed by the whole milk. Simmer for another 10 minutes, or until the stew thickens and the vegetables are fully cooked.
Adjust seasoning and serve: Taste the stew and adjust the salt and pepper if needed. Serve the chicken stew hot, garnished with fresh herbs if desired.