Wash potatoes gently, do not peel. If the potatoes are small, you may keep them whole, otherwise cut them into halves or quarters so all of the pieces are similarly sized.
Trim the green/yellow beans and cut into 1–2-inch lengths.
Put the potatoes in a medium saucepan. Cover with water and 1 tsp of salt; bring to a boil. Cover the pan and reduce the heat to medium-low; cook for 8 minutes.
Add the prepared green beans to the potatoes and continue cooking for 9 to 12 minutes longer, or until both the potatoes and green beans are tender.
Meanwhile, prepare the cream sauce. Melt the butter in a medium saucepan over medium heat.
When the foaming subsides, add the flour. Cook the roux for 2 minutes, stirring constantly.
Gradually whisk the cream or milk into the roux. Cook until thickened, stirring constantly.
Add chopped parsley, if desired.
Taste the sauce and add salt and pepper, as needed.
Once cooked, drain the water off of the potatoes and green beans and transfer the vegetables to a serving dish.
Pour the sauce over the green beans and potatoes and stir gently to coat the vegetables.
