Preheat oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper, leaving an overhang for easy removal.

Prepare the crust: In a medium bowl, combine the flour, 1/4 cup sugar, and salt. Cut in the cold, cubed butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs. Press the mixture evenly into the bottom of the prepared pan.

Bake the crust for 18-20 minutes, or until lightly golden brown. Remove from the oven and set aside to cool slightly while preparing the filling.

Prepare the filling: In a small saucepan, combine the chopped rhubarb, 1/2 cup sugar, cornstarch, and lemon juice. Cook over medium heat, stirring constantly, until the rhubarb softens and the mixture thickens significantly (about 5-7 minutes). Spread the warm rhubarb filling evenly over the pre-baked crust.

Prepare the meringue: In a stand mixer fitted with the whisk attachment, beat the egg whites on medium speed until soft peaks form. Gradually add the remaining 1/2 cup sugar, one tablespoon at a time, beating until stiff, glossy peaks form and the sugar is completely dissolved. Beat in the vanilla extract.

Top the rhubarb layer with the meringue, spreading it evenly to cover completely, ensuring the meringue touches the edges of the crust to seal it in. Return the pan to the oven and bake for an additional 20-25 minutes, or until the meringue is set and lightly golden brown on the peaks.

Allow the bars to cool completely in the pan on a wire rack before lifting out by the parchment overhang and slicing into 12 squares. Store leftovers refrigerated.