Bring a large pot of water to a boil. Add the green beans and cook until they are bright green, about 4 minutes. (This keeps the beans crisp and crunchy, but for more tender beans cook them closer to 8 minutes, or until they are to your liking.) Transfer the green beans to a large bowl of ice water to stop the cooking. Let cool, then drain them and blot dry with a towel.
In a small bowl, whisk together the olive oil, vinegar, shallot, oregano, 1/2 teaspoon of salt, and several grinds of black pepper.
Arrange the green beans and cherry tomatoes in a serving dish. Pour the vinaigrette over the top and toss. Top with the feta.
Serve immediately or store in the fridge for up to 4 days.