Preheat the oven to 425°F. Place the potatoes on a large baking sheet and drizzle with 2 tablespoons of oil. Toss with your hands to coat and sprinkle generously with about ⅔ of the spices.
Toss again with your hands to make sure everything is well coated. Spread the potatoes across the prepared baking sheet and roast for 45 minutes. (Set a timer for 20 minutes.)
While the potatoes begin roasting, prepare the green beans. Place them in a mixing bowl and drizzle with the remaining tablespoon of oil and sprinkle generously with the remaining spices. Toss with your hands to coat well.
After the potatoes have roasted for about 20 minutes, remove them from the oven. Add the green beans to the potatoes, stir with a spatula to combine, and then spread them across the baking sheet.
Return to the oven and roast an additional 20-25 minutes. When the potatoes are tender and slightly crisp, remove from the oven. The green beans should be tender with a slight bite remaining.