Combine flour, baking powder, and salt in a large bowl. Cut in shortening using a pastry cutter or your fingers until crumbly.
In a medium-sized bowl, mix eggs, almost all the ice water, and vinegar. Add egg mixture to the flour mixture and gently mix. As the dough begins to come together, form a ball. Add more water if needed.
Divide the dough into fourths and form each into a disc. Wrap the discs in plastic wrap and refrigerate for at least one hour.
Meanwhile, make the filling. In a medium-sized heavy saucepan, whisk together sugar and cornstarch. In a large bowl, whisk milk and egg yolks. Begin to slowly whisk milk and egg mixture into the saucepan with the dry ingredients. Bring mixture almost to a boil (medium heat) and whisk continuously until thickened, about 8 minutes. Remove from heat. Add butter one tablespoon at a time, allowing each one to melt completely before adding the next, while continuously stirring. Add the extract and slat until combined. Add the bananas and incorporate. Chill until needed.
Sprinkle a work surface with flour and roll a ball of dough out until 1/8-inch thick. Cut it into approximately 4-inch circles. Use a bowl that measures 4-inches across the top. Roll out the remaining discs and repeat. Using all the scraps, form another ball. Roll it out and proceed to cut as many 4-inch circles as possible.
Put about a tablespoon of filling in the center of each circle of dough.
Fold circles in half, wetting your fingers with water to seal the edges. Make sure edges are completely sealed and crimp edges with a fork with flour on it.
Heat about 3 inches of oil in a Dutch oven or deep frying pan. Heat the oil to 375 degrees.
Fry two pies at a time until golden brown on both sides, about 2 minutes per side. Drain on paper towels.
Sprinkle with powdered sugar and serve with whipped cream.