Preheat the oven to 425 degrees F. Place a baking sheet in the oven to preheat while you prepare the potatoes.
Toss the potatoes with the oil and thyme on a baking sheet and season liberally with salt and pepper. Roast the potatoes until golden brown and crisp on the outside but fork-tender on the inside, 15 to 18 minutes. Transfer to a large bowl and toss with the feta and green onions. Serve immediately.