Preheat the air fryer to 380°F.
Rinse 16 ounces fresh green beans in a colander, then pat them dry thoroughly with a clean towel or paper towels so the flour will adhere.
Put 1/4 cup all-purpose flour in a shallow bowl.
Crack 2 large eggs into a second shallow bowl and whisk until smooth.
In a third shallow bowl, stir together 1 cup panko bread crumbs, 1/2 cup grated Parmesan cheese, 1/2 teaspoon salt, and 1/2 teaspoon freshly ground black pepper.
Working in batches that will fit in a single layer in your air fryer basket, coat the green beans: lightly toss a few beans in the flour and shake off excess, dip them into the whisked eggs, then press them into the panko-Parmesan mixture so they are evenly coated. Place the coated beans in a single layer in the basket without overlapping.
Air fry at 380°F for 5 minutes. Open the basket, gently shake or flip the beans to promote even browning, then continue air frying 1–2 more minutes (total 5–7 minutes) until the beans are golden brown and crisp. Check at 5 minutes and adjust time as needed for your air fryer.
Remove the cooked green beans to a plate, then repeat coating and air frying with any remaining beans. Serve warm with your favorite dipping sauce.