Preheat oven to 450°F. Coat a 15x10x1-inch baking pan with the 2 teaspoons oil; set aside.
In a large bowl combine the flour and 1/8 teaspoon of the salt. Add green beans and toss to coat.
In a shallow dish combine the panko and remaining 1/8 teaspoon salt. In another shallow dish place the eggs. A few at a time, dip green beans in the eggs to coat, then roll in panko to coat (tip: to prevent the crumbs from getting to wet, work with half of the panko at a time).
Arrange beans in a single layer in the prepared pan. Drizzle with sesame oil. Bake for 10 to 12 minutes or until golden.