Slice the potatoes into quarters lengthwise, then cut across into ¼ inch slices. Place the sliced potatoes in a pot and cover with water. Bring the pot to a boil over high heat, then let simmer until the potatoes are tender (about 5 minutes). Check the potatoes with a fork often, making sure not to over boil them. They should be easily pierced with a fork, but not so soft that they fall apart. Drain the potatoes in a colander.
While the potatoes are boiling, snap the stems off of the green beans, then break them into 1-2 inch sections. Rinse with cool water to remove any dirt or debris.
Mince the garlic and onions and add it to a large skillet along with the olive oil. Sauté the garlic over medium heat for about one minute, then add the drained potatoes. Continue to sauté the potatoes, stirring only once every 3-5 minutes, until about half of them are golden brown (5-10 minutes).
Add the green beans to the skillet and continue to sauté until they are slightly softened and have some browned spots (about another 5 minutes). Season the skillet with salt, Italian seasoning, and oregano. Sauté for one minute more, then serve.