Preheat your oven to 400 degrees Fahrenheit. While the oven is heating up, line a large rimmed baking sheet with parchment paper or a silicone baking mat.
Place the trimmed green beans into a large mixing bowl. Drizzle the olive oil over the beans and add the minced garlic, salt, pepper, and smoked paprika. Toss everything together with your hands or tongs until every single bean is evenly coated in the oil and spices.
Sprinkle the grated Parmesan cheese and the panko breadcrumbs over the seasoned beans. Toss the mixture one more time, very gently, to help the cheese and crumbs adhere to the oil on the beans.
Spread the green beans out in a single layer on the prepared baking sheet. Roast in the oven for 18 to 22 minutes, tossing halfway through, until the beans are tender and the Parmesan crust is golden brown and crunchy.
