Prepare the vegetables:
Wash and trim the green beans, then cut the potatoes into small cubes for even cooking.
Sauté the onion and garlic:
Heat olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and cook for 3–4 minutes until softened. Add the minced garlic and sauté for another 1–2 minutes until fragrant.
Cook the potatoes:
Add the cubed potatoes to the pot, along with thyme, rosemary, salt, and pepper. Stir to combine, then cook for 5 minutes, stirring occasionally, until the potatoes begin to soften slightly.
Add the broth and green beans:
Pour in the chicken or vegetable broth, then add the green beans. Stir everything together, cover the pot, and bring the mixture to a simmer.
Simmer:
Reduce the heat to low and let everything simmer for 15–20 minutes, or until the potatoes are tender and the green beans are cooked through. Stir occasionally, and check the seasoning, adding more salt and pepper if needed.
Finish with butter:
Once the vegetables are tender and the flavors have melded, stir in the butter until melted and creamy.
Serve:
Garnish with chopped fresh parsley, if desired. Serve hot as a side dish alongside your favorite main course!