Prepare the pastry by combining the flour and salt in a bowl. Rub in the butter and shortening until incorporated, and the mixture takes on a sandy appearance. Combine egg and water, and stir into the flour mixture until a dough forms, then knead for a few turns to bring the dough together. Wrap and chill for three hours in the refrigerator.
While the dough is chilling, peel plantains and cut into thirds. Place into a small saucepan with a little water. Bring to a simmer and steam until tender, five to ten minutes depending on how ripe your plantains are. Once soft, pour out the water, and mash plantains with sugar, vanilla, nutmeg, and red food colouring. Set aside to cool.
Preheat oven to 350°F (175°C).
Roll dough out on a lightly floured surface to six millimeters thick. Cut into circles using a four- or five-inch round cookie cutter. Spoon a little of the plantain filling into the centre of each circle, then fold in half, to form a half-moon shape. Place the tarts on a baking sheet, brush with beaten egg white, and sprinkle with sugar.
Bake in preheated oven for 20 to 25 minutes until golden brown. Allow tarts to cool to room temperature before serving.
Instead of using red food coloring you can boil one small beet with your plantin and mash it along with the remaining ingredients.