Preheat oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Wash, dry, and cut potatoes into even pieces.
Place potatoes on the pan, add 2 tbsp oil and seasonings, and toss well.
Spread potatoes in a single layer and roast for 15 minutes.
While potatoes cook, wash, trim, and dry green beans.
Remove pan, add green beans, garlic, and remaining oil.
Toss everything gently to combine.
Spread evenly and return to oven.
Roast for 20 more minutes, tossing halfway if needed.
Cook until potatoes are golden and beans are tender.
Taste, adjust seasoning, and serve warm.