Preheat oven to 425F. Lightly grease a parchment-lined baking sheet and set aside.
In a bowl, combine crushed crackers, parmesan, garlic powder, and cayenne powder. In a separate bowl, whisk eggs until combined.
Dip each green bean in the egg mixture first, and coat well in the cracker mixture. Place them on the baking sheet and bake for about 10-12 minutes, or until the beans are tender and the crust is golden.
Combine all sauce ingredients in a bowl, and serve with the crispy green bean fries.