Preheat your oven to 400°F and line a large baking sheet with parchment paper or foil for easy cleanup. While the oven heats, cut the potatoes into 1-inch chunks for even roasting—uniform size is key so everything cooks at the same rate. Trim the green beans and snap them into 2-inch pieces. Chop the fresh parsley and set aside for garnish at the end.
In a large bowl, toss the cut potatoes with 2.5 tablespoons olive oil, Italian seasoning, 0.75 teaspoon salt, 0.25 teaspoon onion powder, and a generous grind of black pepper. Spread the potatoes in a single layer on the prepared baking sheet and roast for 20 minutes. I like to use extra virgin olive oil for roasting because it adds a subtle richness that enhances the potato flavor. Starting the potatoes first ensures they have enough time to develop a golden, crispy exterior.
After 20 minutes, remove the baking sheet from the oven and give the potatoes a stir to flip them for even browning. In a bowl, toss the green beans with 1.5 tablespoons olive oil, 0.5 teaspoon garlic powder, and 0.5 teaspoon salt. Spread the seasoned green beans across the same pan with the potatoes, then return to the oven and roast for another 25 minutes until the potatoes are golden and tender and the green beans are lightly charred. I find that adding the green beans halfway through prevents them from drying out while still allowing them to get slightly caramelized at the edges.
Remove the baking sheet from the oven and immediately sprinkle the 1/3 cup grated Parmesan evenly over the roasted vegetables while they're still hot—the residual heat will help it adhere and create a slightly crispy, salty crust. Scatter the chopped fresh parsley over the top for a fresh, bright finish.
Transfer the roasted vegetables to a serving dish or plate while still warm to preserve the crispiness. Serve immediately while the Parmesan is still at its best.