Preheat your oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper, allowing some overhang for easy removal later.
In a food processor, combine flour, sugar, and salt with a quick pulse. Add the cold butter cubes and pulse until the mixture resembles coarse crumbs (about 10-12 pulses). Add ice water and pulse just until the dough begins to come together.
Press the dough evenly into the bottom of your prepared pan, using the flat bottom of a measuring cup to create a smooth, even surface. Bake for 15 minutes until the edges are just beginning to turn golden. Remove from oven but keep the oven on.
While the crust bakes, whisk together sugar, eggs, flour, vanilla extract, and salt in a large bowl until smooth and well combined. Gently fold in the chopped rhubarb (and strawberries if using), ensuring each piece gets coated with the mixture.
Pour the rhubarb mixture over the warm pre-baked crust, spreading it evenly to the edges. Bake for 30-35 minutes, or until the filling is set and no longer jiggles in the center when gently shaken.
Allow the bars to cool completely in the pan for at least 2 hours or overnight in the refrigerator. Once cooled, use the parchment overhang to lift the bars from the pan and cut into 16 squares.