Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking pan; a light spray with cooking oil or a thin layer of butter works perfectly.

In a medium bowl, combine 1.5 cups all-purpose flour and 0.5 cup granulated sugar. Add the cold cubed butter and cut it in with a pastry blender, a fork, or your fingertips until the mixture resembles coarse crumbs. Press this mixture evenly into the bottom of the prepared baking pan. Bake for 15-18 minutes, or until the crust is lightly golden around the edges.

While the crust is baking, prepare your rhubarb filling. In another medium bowl, gently toss the chopped rhubarb with 0.5 cup granulated sugar, 2 tablespoons all-purpose flour, and 1 tablespoon fresh lemon juice. Set this aside.

In a separate bowl, whisk together the 3 large eggs, 0.75 cup granulated sugar, 0.5 cup heavy cream, 1 teaspoon vanilla extract, and 0.25 teaspoon salt until everything is well combined and slightly frothy. You're aiming for a smooth, uniform mixture here.

Once the shortbread crust has finished its initial bake, carefully remove it from the oven. Reduce the oven temperature to 350°F (175°C). Evenly spread the prepared rhubarb mixture over the warm crust. Then, carefully pour the custard topping over the rhubarb, ensuring it covers everything nicely.

Return the pan to the preheated 350°F (175°C) oven and bake for another 35-45 minutes. The bars are ready when the custard is set (it shouldn't jiggle much in the center) and the edges are lightly golden. A knife inserted near the center should come out clean. Let the bars cool completely on a wire rack at room temperature.

Once cooled to room temperature, transfer the pan to the refrigerator and chill for at least 2 hours before cutting into squares and serving. Chilling helps the bars set perfectly and makes for cleaner slices.