Preheat the oven to 375°F (190°C). Lightly butter an 8x8-inch or 9x9-inch baking dish and set aside.
Prepare the rhubarb. Wash and trim the rhubarb stalks, removing all leaves (they are toxic — discard them). For thicker stalks, peel away any tough fibrous strings with a paring knife. Cut into ½-inch pieces until you have 4 cups.
Make the filling. In a large bowl, combine the rhubarb, granulated sugar, cornstarch, lemon juice, lemon zest, cinnamon, and vanilla extract. Toss until the rhubarb is evenly coated. Pour into the prepared baking dish and spread into an even layer.
Make the crisp topping. In a medium bowl, stir together the rolled oats, flour, brown sugar, cinnamon, and salt. Add the cold butter cubes and use your fingertips to work the butter into the dry ingredients until the mixture forms coarse, uneven crumbles with some pea-sized chunks. Do not overmix.
Assemble. Scatter the oat topping evenly over the rhubarb filling, covering all the way to the edges of the dish.
Bake on the center rack for 40–45 minutes, until the topping is deep golden brown and the filling is bubbling around the edges. If the topping browns too quickly, tent loosely with foil for the last 10 minutes.
Cool and serve. Let the crisp rest for at least 15–20 minutes before serving to allow the filling to thicken. Serve warm with vanilla ice cream or whipped cream.