Prep the green beans by trimming the ends. Add to a steamer and steam the beans until tender to your liking, about 5-10 minutes. We like green beans to be pretty tender, so I allow them to steam for a good 10 minutes. If you prefer, you could skip the steaming process and sauté the green beans for 10 minutes prior to adding the onions.
Heat a large skillet on medium heat. Add oil, then add the onions and cook until soft and lightly browned, 3-5 minutes.
Add the steamed green beans to the skillet and sauté them for 3-5 minutes.
Whisk together the sour cream, parmesan cheese, milk, salt, and pepper in a bowl or measuring cup. Add the mixture to the skillet.
Heat the skillet over medium heat, allowing the sauce to get to a good simmer. Allow to simmer for about 5 minutes, stir occasionally as the sauce thickens and coats the green beans.