Heat the oven to 450°F.
Lightly coat rectangular baking sheet with coconut oil.
Beat the eggs and water with a fork in shallow bowl. Mix the flour, salt, and pepper in separate shallow dish.
Dip 5-6 vegetable pieces into egg mixture, then remove them and roll them immediately in the flour mixture to coat. Place them in the prepared pan and repeat with the remaining vegetables.
Drizzle melted butter over the veggie pieces then bake uncovered 12-15 minutes, turning once, until vegetables are tender and coating is light golden brown.