Combine flour and salt in a bowl; rub in butter and shortening until incorporated, and mixture takes on a sandy appearance. Combine whole egg and water; stir into flour mixture until a dough forms. Transfer to a work surface; knead dough for a few turns to bring together. Wrap well in plastic wrap; chill in the refrigerator for 3 hours.
While dough chilling, peel plantains; cut into thirds. Heat in a saucepan with a little water; bring to a simmer. Steam until tender, 5 to 10 minutes (depending on how ripe your plantains are). Once soft, discard water; mash plantains with 1/4 cup sugar, vanilla, nutmeg, and food coloring. Set aside to cool.
Preheat the oven to 350 degrees F (175 degrees C).
Roll dough out on a lightly floured surface to 1/4-inch thick. Cut into circles using a 4- or 5-inch-round cookie cutter. Spoon a little plantain filling into center of each circle; fold in half, to form half-moon shapes. Place tarts on a baking sheet; brush with beaten egg white and sprinkle with sugar.
Bake in the preheated oven until golden brown, 20 to 25 minutes. Allow tarts to cool to room temperature before serving.
