Add 2 more teaspoons of oil to the same pan and heat it over a medium-high heat. Add the onions, carrots and celery and cook until the vegetables begin to soften, about 3 minutes. Add the green beans, garlic and remaining salt and pepper and cook for 2 minute more. Add the milk. Stir the flour into the broth until it is completely dissolved and add to the pan. Cook, stirring, until the mixture comes to a boil. Reduce the heat to medium-low and cook for 2 minutes more.