In a large bowl blend together the flour, the butter, the shortening, the coconut, and a pinch of salt until the mixture resembles meal. Add 1 1/2 tablespoons ice water, toss the mixture until the water is incorporated, and form the dough into a ball. Flatten the dough slightly, dust it with flour, and chill it, wrapped in wax paper, for 1 hour. Divide the dough in half and roll out each half 1/8 inch thick on a lightly floured surface. Fit each half into a 4 1/4-inch tartlet pan and roll a rolling pin over the pan edges to trim the excess dough. Prick the shells with a fork and bake them in a preheated 425°F. oven for 5 minutes. Reduce the heat to 375°F. and bake the shells for 12 to 15 minutes more, or until they are golden. Transfer the shells to a rack and let them cool. The shells may be made 1 day in advance and kept in an airtight container. In a saucepan combine the milk and 2 tablespoons of the sugar and bring the mixture just to a boil over moderate heat. In a bowl whisk together the yolk, the vanilla, the banana, mashed, the remaining 1 tablespoon sugar, the flour, and a pinch of salt. Add half the milk mixture in a stream, whisking, pour the egg mixture into the pan, and bring the mixture to a boil, whisking constantly. Simmer the custard for 1 minute, remove the pan from the heat, and whisk in the butter. Force the custard through a fine sieve set over a bowl, cover its surface with plastic wrap, and chill the custard for 2 hours. The custard may be made 8 hours in advance and kept covered and chilled. In a bowl beat the cream until it holds soft peaks and fold it gently but thoroughly into the custard. Divide the filling between the shells and arrange the strawberries decoratively on it. In a small saucepan melt the jelly with the lemon juice over moderate heat and brush the strawberries with the glaze. Sprinkle the tartlets with the toasted coconut.