1. Stir together 1 tablespoon flour and 1/4 cup water in a small bowl until flour is dissolved; set aside.

2. Heat oil in a large skillet over medium heat until hot but not smoking. Add onion and garlic; cook, stirring occasionally, until onion is soft but not brown, about 2 minutes. Add shrimp and tomato paste; season with salt and black pepper. Cook, stirring occasionally, until shrimp are cooked through and opaque, about 3 minutes. Stir in cayenne and parsley. Stir in flour mixture; simmer 2 minutes. Turn off heat; stir in olives. Season again with salt and pepper. Set aside.

3. Preheat oven to 375 degrees. Place remaining 4 cups flour in a large bowl; make a well in the center. Place butter, mayonnaise, eggs, milk, and 2 teaspoons salt in well. Squeeze wet ingredients between fingers of one hand to combine. Gradually work in flour, squeezing to form a soft dough.

4. Pinch off 60 cherry-size balls of dough; reserve leftover dough. Set aside 15 dough balls. Transfer remaining 45 dough balls to baking sheets. Wrap in plastic; refrigerate. Divide reserved dough into 4 pieces; set aside 1 piece. Wrap remaining 3 pieces in plastic; refrigerate.

5. Transfer reserved dough balls to fifteen round tartlet molds (each 1 1/2 inch diameter by 1/2 inch high). Press down dough; it should reach just over tops. Mound 1 teaspoon filling in each mold.

6. Roll out a dough piece to 1/8 inch thick. With a 2-inch round cookie cutter, cut out 15 tops. Place over filling, pressing edges of dough to seal; trim excess. Transfer to a baking sheet. Brush tops with egg glaze. Repeat process with remaining dough balls, filling, and divided dough pieces.

7. Bake empanadas until cooked through and golden brown, 25 to 30 minutes. Let cool slightly on a wire rack; unmold. Serve warm or at room temperature.