In a bowl, sift together the flour, light brown sugar, cinnamon, and salt. Cut in the butter until the mixture resembles coarse crumbs. Sprinkle with the ice water, and toss the mixture with a fork until evenly moistened. Pat into a round, and wrap in plastic. Refrigerate for 30 minutes.
In the top half of a double boiler, heat the milk until it begins to bubble. In a bowl, beat together the egg whites, sugar, and 1 tablespoon of the hot milk. Whisk the egg white mixture into the remaining hot milk . Cook and stir without boiling about 10 minutes, until the mixture is thick enough to coat the back of a metal spoon. Remove from heat, and stir in the vanilla. Cool to room temperature.
Preheat oven to 375 degrees F (190 degrees C). Lightly grease an 8 inch tart pan with a removable bottom.
On a floured surface, roll the tart dough out to 1/4 inch thickness. Press the chilled dough into the prepared tart pan. Trim the edges, and pierce the bottom with a fork. Bake 15 to 18 minutes in the preheated oven, until golden brown. Remove to a wire rack, and cool completely.
Spoon the filling mixture into the crust. Bake 18 to 20 minutes in the preheated oven. Cool to room temperature on a wire rack. Refrigerate 8 hours. Arrange banana, kiwi, and strawberry slices over the filling just before serving.