To prepare dough: On a lightly floured piece of parchment paper, roll out the dough to a 12-inch square, about 1/8-inch thick. With a dry pastry brush, sweep off excess flour; fit dough into a 9-inch square fluted tart pan with a removable bottom, pressing into corners. Using a sharp knife or rolling pin, trim dough flush with pan. Prick the bottom of the dough all over with a fork. Chill tart shell until firm, about 30 minutes.
Preheat oven to 350 degrees. Line chilled shell with parchment paper, leaving at least a 1-inch overhang. Fill with pie weights or dried beans. Bake until edges are just beginning to turn golden, 20 to 25 minutes. Remove parchment and weights; continue baking until crust is deep golden brown all over, 10 to 15 minutes. Remove from oven to a wire rack and cool completely.
To prepare rhubarb: In a large skillet, stir together 1 1/2 cups water, 1 1/2 cups sugar, vanilla bean and seeds and beet. Cook over medium-high heat, stirring occasionally, until sugar is completely dissolved and mixture comes to a boil. Add rhubarb, turn off heat. Cover and let stand until rhubarb is tender and gives only slight resistance when pierced with the tip of a sharp paring knife, about 20 minutes. Line a baking sheet with several layers of paper towels. Carefully remove rhubarb from skillet with a slotted spoon, and spread in a single layer on prepared baking sheets. Strain 1 cup of poaching liquid into a medium skillet. Cook over high heat until syrup has thickened to a glaze, about 10 minutes; set aside until cool. To prepare filling: In a bowl of an electric mixer, combine cream cheese, remaining 2 tablespoons sugar and lemon zest and beat until smooth. Add sour cream and beat until mixture is very smooth.
To assemble tart: Using an offset spatula, spread cream cheese mixture evenly over bottom of cooled crust. Carefully arrange poached rhubarb on top of the cream cheese mixture and drizzle with reserved cooled syrup. Loosely cover with plastic wrap and chill in refrigerator until ready to serve, up to 4 hours.
Enough for 1 9-inch tart.