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Step 1
Make the rhubarb: Position a rack in the center of the oven and preheat to 350°F. In a pie plate or 8-by-8-inch baking pan, toss the rhubarb, sugar, salt, and beet if using. Bake until the rhubarb is soft and spreadable, stirring halfway through baking, about 1 hour 5 minutes. Discard the beet. (Leave the oven on.)
Step 2
Meanwhile, make the crust: In a medium bowl, whisk together the flour, quick oats, and baking soda. To a food processor, add the salt, sugar, and eggs and blend until combined, about 2 minutes. Add the flour and pulse to combine, then scatter with the butter and pulse until the dough is uniform and no butter pieces are visible. Transfer three quarters of the dough to a greased 9-by-13-inch sheet pan and press into an even layer. Scrape the remaining dough into a bowl and set aside. (Do not clean the food processor.)
Step 3
Make the crumble: In a small bowl, whisk together the milk and yolks and set aside. To the empty food processor, add the flour, brown sugar, butter, quick oats, and rolled oats and pulse until a crumbly, shaggy mass forms.
Step 4
Assemble the rhubarb bars: Turn the oven to 325°F. Spoon the rhubarb and its juices in an even layer atop the dough, then sprinkle the remaining dough evenly over the top. Drop the crumble in large, irregular chunks over all, then brush evenly with the yolk mixture.
Step 5
Bake until the rhubarb bars are firm and lightly browned on top, about 40 minutes. Cool to room temperature before cutting into squares (as large or as small as you like).