Preheat the oven to 375°F. Line a baking sheet with parchment paper.
Wash and cut the potatoes in cubes, halves, or quarters, depending on their size, just make sure the potato pieces are about the same size so they cook evenly. Place in a big bowl or pot and cover with hot water. Set aside for 3-5 minutes, then drain carefully.
Place drained potatoes on the lined baking sheet and drizzle with olive oil. Season with thyme, basil, oregano, salt, and pepper. Stir to fully coat potatoes. Add rosemary sprigs. Roast for 20 minutes.
Meanwhile, rinse and trim the green beans. Bring a large pot of water to a boil. Place the beans in the boiling water and cook for 5 minutes. Drain.
Remove potatoes from the oven and combine with green beans. Give it a good stir so the spices can also cover the green beans. Place all the veggies back in the oven and bake for 15 minutes, until golden and cooked through.
Remove from the oven, add minced garlic while the veggies are still hot, and stir. Transfer to a serving bowl and serve immediately.