Make the dough: In a large bowl mix flour, baking powder, and salt. Cut in butter until coarse crumbles form. Add egg and water, stirring and kneading until a dough forms. Cover in plastic wrap and refrigerate dough for at least 30 minutes. Roll out dough on a floured surface to 1/8 inch thick. Using a biscuit cutter, cut out rounds for empanadas. Set aside.
Make the filling: In another bowl combine peppers, onion, fries, plantain, and chicken. Toss to evenly distribute ingredients.
Assemble empanadas: Preheat oven to 350 F. Line baking sheet with baking mat and set aside. In another small bowl whisk eggs. Set aside.
Using one disc at a time, brush round with egg them place 2 tablespoons of chicken filling in center. Fold dough over, then press edges together with fingertips or with a fork to close. Place empanada on baking sheet and repeat with remaining dough and filling. Once all empanadas are made, brush each one with egg wash. Transfer empanadas to oven and bake for 15-20 minutes, until golden brown and fluffy.
Serve immediately with pico, sour cream, and lemon and lime wedges.