Preheat the oven to 400°F. Line a large rimmed baking sheet with nonstick cooking spray; set aside. Place the potatoes in a large bowl or zip-top plastic bag. Add 1 tablespoon of olive oil, ¼ teaspoon garlic powder, and ¼ teaspoon salt. Toss gently to evenly coat the potatoes. Spread the potatoes onto the prepared baking sheet (reserve the bowl or plastic bag so that you can use it again with the green beans). Roast the potatoes in the oven for 15 minutes, stirring once.
While the potatoes are in the oven, place the green beans in the large bowl. Add 1 tablespoon of olive oil and ¼ teaspoon salt. Toss gently to coat the green beans.
After the potatoes have been roasting for 15 minutes, remove the baking sheet from the oven. Spread the green beans onto the baking sheet with the potatoes in a single layer.
Return the baking sheet to the oven and roast the potatoes and green beans for about 10-15 more minutes (stirring halfway through), or until the vegetables are tender. Keep an eye on the potatoes, because very small potatoes will be done in about 20 total minutes, while larger potatoes will need closer to 30 minutes. They should be crispy on the outside and fork-tender on the inside. Season with additional salt and pepper, if necessary. Set the potatoes and green beans aside to cool slightly while you assemble the rest of the salad ingredients.