In a large pot over medium heat, add a splash of olive oil and then toss in chopped onions, diced carrots, and celery. Sauté for about 5 minutes, stirring occasionally, until the vegetables are softened and aromatic.

Add minced garlic to the pot and cook for an additional 1 to 2 minutes, stirring until the garlic becomes fragrant but not browned.

Pour in the chicken broth, ensuring you scrape any bits sticking to the bottom of the pot. Increase the heat and bring the mixture to a boil.

Add diced potatoes to the boiling broth, seasoning with salt and pepper to taste. Reduce the heat to a simmer and cover the pot, allowing it to cook for about 20 minutes.

After 20 minutes, stir in your choice of green beans and any pre-cooked meat, let everything heat through for an additional 5 minutes.

Before serving, taste your soup and adjust the seasoning, adding more salt or pepper as needed.