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1. For the pastry cream: Pour the milk and 2 tablespoons of the sugar into a 1 1/2-quart saucepan. Split the vanilla bean with a small knife, scrape out the seeds and add the seeds to the milk. Place the egg yolks in a small bowl and whisk to combine. Whisk in the remaining sugar. Then stir in the flour and set aside.
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2. Bring the milk mixture just to a boil over medium heat. Turn off heat and pour about half the milk mixture into the yolk mixture, whisking until combined. Pour the mixture back into saucepan; whisk to combine; then return to medium-low heat. Cook, stirring constantly, until the mixture comes to a boil (about 1 to 2 minutes). At this time it will thicken. Continue to stir and simmer until it is smooth and thick (for about 1 minute). Remove from heat and add the butter, stirring until incorporated.
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3. Rest a sieve on top of a 1-quart mixing bowl to strain the cooked pastry cream. Pour the cream through the sieve into the mixing bowl. Cover the surface of the pastry cream with plastic wrap, and poke 6 to 8 slits in it with the tip of a knife to allow steam to escape. Refrigerate for up to 3 days.
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Fill and serve the tart the day it is baked.
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10. To assemble: Lightly sprinkle the tart's border with powdered sugar. Spread chilled pastry cream over the bottom of the tart shell. Arrange the strawberry pieces, cut sides up and stem ends facing out toward the edge of the tart, in concentric circles, overlapping, if you like. To glaze the berries, heat the jelly and 2 teaspoons water in a small saucepan, just until it's melted and warm, not hot. Stir in the rose water, if using, and brush the glaze all over the fruit to preserve the berries fresh appearance. Refrigerate the tart until about 45 minutes before serving.
