Preheat oven to 425°F. Line a large baking sheet with parchment paper or a silicone baking mat.
In a shallow bowl or small baking dish (large enough for the beans to roll), combine 2 cups Panko bread crumbs, 1/3 cup grated Parmesan cheese, 1/4 teaspoon garlic powder, 1/4 teaspoon kosher salt, and 1/4 teaspoon freshly ground black pepper; stir until evenly mixed.
Crack 2 eggs into a separate shallow dish and whisk until smooth and combined.
If needed, pat 1 pound fresh green beans dry. Working in batches of 3–4 beans, dip the beans into the whisked eggs, letting any excess egg drip off, then roll them in the Panko mixture until well coated.
Arrange the coated green beans in a single layer on the prepared baking sheet, leaving a little space between each so they can crisp.
Evenly drizzle 2 tablespoons olive oil over the coated green beans on the baking sheet.
Bake in the preheated oven for 15–20 minutes, until the beans are tender and the coating is golden brown (check at 15 minutes and continue up to 20 minutes as needed).
Remove from the oven, squeeze the juice from one small lemon over the fries if using, and season with additional kosher salt to taste. Serve immediately.