Preheat the oven to 400 degrees F. Spray or line a baking sheet.
In a small bowl, mix together the flour and paprika. In another small bowl, whisk the egg. In another small bowl, mix together the breadcrumbs, parmesan cheese, salt and pepper (if using).
One at a time, add a piece of chicken to the flour and toss until coated, shaking off any excess flour. Then dip the chicken into the egg until coated. Then toss the chicken into the breadcrumb mixture until completely coated. Place the finished nugget on one side of the baking sheet. Continue this process until all of the chicken pieces are coated and are on one side of the baking sheet.
In a medium bowl, toss together the green beans, oil, parmesan cheese, breadcrumbs and garlic powder. Place the green beans in a single layer on the other side of the baking sheet as the chicken nuggets.
Bake for 18-20 minutes, flipping half way through baking time, or until the chicken nuggets are golden brown and cooked all the way through.